The scene is now set for an extraordinarily delicate and high-stakes fortnight of negotiations. It is high noon, and fingers are on a hair-trigger.
There are two burning issues: the Irish backstop, and a political declaration on the future EU-UK relationship.
Both are highly charged politically and legally, and both are - to a disputed extent - dependent on each other.
The EU now wants to secure "maximum progress" on both issues at the October European Council, so that an over-arching deal can be done at an emergency summit on the weekend of 17-18 November.
"The aim is to fold in all the dimensions of the problem in October," says a senior EU official, "and then iron out the rest, finalise everything by the [November] summit. It may not be possible to do everything in one go in October."
But the signs are that fundamental differences remain between the EU and the UK on the backstop. These are differences of law, politics and timing.
It is understood the UK will harden its position that it will not sign up to a backstop unless the British government is satisfied with what is contained in the political declaration on the future relationship.
Furthermore, it remains a red line for the UK that Northern Ireland must not be left in a different "customs territory" from the rest of the UK.
While numerous elements are already conspiring against a successful outcome - the disaster of Salzburg, the lack of time, the chaos within the Conservative Party - these red lines keep the UK and Ireland and the EU on a collision course.
Both sides are expected to bring forward fresh proposals on the backstop after the Tory Party Conference, but how they do that and when will be critical.
"There needs to be choreography here," says a senior diplomat from one member state, "otherwise you risk a serious breakdown in negotiations."
The impact of Salzburg continues to resonate.
The EU narrative remains that Theresa May was largely responsible for the car crash by raising expectations that leaders would throw Chequers a lifeline, by trying to reach over the head of Michel Barnier to leaders, by striking an aggressive "I’ve moved, now you must move" posture, and by rejecting out of hand Michel Barnier’s efforts to de-dramatise the backstop.
Downing Street’s view is that European Council President Donald Tusk’s blunt rejection of the economic and trade elements of Chequers created ill-will and seriously damaged the role that Chequers was supposed to play in the creation of the political declaration.
And because London believes in a strict conditionality between the backstop and the political declaration, it regards Salzburg as a serious setback for a solution on the backstop.
Some EU officials are looking for comfort wherever it can be found.
"It was probably better to have that [controversy] in September, rather than October," says a diplomat from one member state. "People may have forgotten it by the time of the Council."
Others are more circumspect.
Theresa May’s hardline, show-me-some-respect statement the day after Salzburg was seen as entirely for domestic consumption, but it is still a case of running to stand still.
"There’s a feeling that May has steered her boat into slightly more manageable waters [domestically]," says one senior official close to the negotiations.
"We’re not expecting things to completely crumble before the Tory Party Conference - but we’re not expecting any movement from the British side either."
That means everything is very delicately poised.
From an Irish point of view, the backstop is further complicated in that it requires legal certainty.
"Making it really watertight means we’re really into wonk territory now," says a senior Irish figure. "The question is: is there a way in which technical experts can engage, privately, but also in a not too politically charged atmosphere?"
The source adds: "People might think we can work something out, but then it turns out later on that we discover we missed something, or that people thought it would work in a certain way and then suddenly it doesn’t.
"That’s no good to us. This has to provide legal certainty, so it has to be tested quite rigorously."
As things stand, Ireland and the EU are seeking a legally operable, all-weather backstop that will form part of the Irish Protocol in the Withdrawal Agreement.
Michel Barnier has told member states that if the backstop comes into effect, the EU would be prepared to lighten the frequency and degree of checks on goods coming from Britain to Northern Ireland, with only live animal and agri-food shipments requiring physical checks at UK and Northern Irish ports.
Britain is adamant that Northern Ireland cannot be in a separate customs territory, and it regards Michel Barnier’s offer as "window-dressing".
Any customs backstop must be UK-wide. Otherwise, there would be a customs border along the Irish Sea.
RTÉ News has obtained a clearer picture from a number of different sources of the bilateral meeting between Theresa May and Leo Varadkar in the Sheraton Grand Hotel in Salzburg at 8.30am last Thursday morning.
By all accounts this was a more cordial gathering relative to previous encounters, notably in Sofia on 17 May, and last November in Gothenburg.
Neither side had any warning of the flare-up that would take place that afternoon.
The Taoiseach first made it clear that Dublin was unhappy that the UK side was not going to move substantially in October.
While the whole thing wouldn’t be sorted in one go, without substantial agreement then EU leaders would be faced with trying to agree a difficult legal text in the small hours in November.
"The Irish Protocol is a detailed, complex, legal text," says one source present.
"The idea that you’ll have leaders sitting in the room at three in the morning, hammering out last minute tweaks is just not clever, apart from any wider political concerns."
Theresa May was unmoved.
The Prime Minister insisted the whole deal had to be done as a package, and there wasn’t enough time to get it done at the October summit. "She wasn’t committing to anything sequentially," says the source.
Despite this the mood remained constructive. "Everyone then agreed we’d need to work together as quickly as possible because there wasn’t a lot of time left," says the source.
There followed a more general discussion on the backstop and how things could be moved forward.
The British delegation, which included Theresa May’s Europe advisor Olly Robbins, Chief of Staff Gavin Barwell, and the UK’s Permanent Representative to the EU Tim Barrow, indicated that London would bring forward new proposals shortly on the backstop.
Again, the Irish delegation responded positively, but with a note of urgency.
"We said, the sooner you get that into Barnier the better as that’s the right channel.
"We said we will of course consider anything you put forward and we’ll talk to the Task Force, and, within reason, if it does the job we all want it to do…, we’re not ideologically wedded to one format over another."
It has since become clear that the UK is hardening its position on two fronts.
Both issues explain Theresa May’s reticence about the October summit, and her dismissal of the "de-dramatisation" proposals, as yet untabled, from Michel Barnier.
Firstly, London now sees an explicit conditionality between the backstop and the future relationship.
The UK has all along argued that the Irish border would, and should, be resolved through the future trade relationship.
That was the British government’s main counter-argument to the backstop.
Ireland and the EU agreed that the border might be solved in the future relationship – but they couldn’t take that chance.
If they did, the border would become a pawn in trade talks, they argued.
The backstop was simply a guarantee that whatever happened, there would be no hard border.
And that guarantee would have to be written in to the divorce and made legally operable.
It now looks clear that the political declaration will be a mountain for negotiators to climb.
According to a senior official, the EU has three overriding priorities when it comes to the political declaration.
One is make sure that Theresa May signs up to the Withdrawal Agreement, secondly to make it very clear that the future EU-UK relationship is going to be substandard compared to membership, and thirdly to ensure that it is as clear and detailed as possible so that actual trade negotiations when they start after the end of March 2019, do not get snarled up in disagreements over what the remit is.
But the political declaration is a two-way street.
"It’s a joint political declaration," says one EU diplomat. "It’s not one sided. That will need to be sorted out."
EU sources accept that the backstop and the political declaration are linked.
But there is a vital difference: one is legal, the other is aspirational.
So, for Dublin and Brussels the absolute minimum is that the backstop is in the Withdrawal Agreement and watertight, while the political declaration will spell out options for the future that might, depending on how closely the UK cleaves to the EU’s regulatory orbit, mean the backstop is never needed.
"It will be very hard to solve Ireland without solving the economic core of the future framework," says one senior EU source, "so they would need to go hand in hand: you can’t solve one without the other."
But that doesn’t necessarily mean the political declaration gives Theresa May the same legal certainty that the Withdrawal Agreement will provide on the backstop.
"It’s more a question of the direction of travel. The backstop is for now. It’s got to be legally binding. But to be able to get an agreement on the backstop, you can’t do it in a vacuum. You would need the Prime Minister to be able to go back and say, I’m confident we can get somewhere on the political declaration."
But from a UK perspective, the whole point of Chequers, and why Theresa May has clung to it, is that its economic parts – the common rulebook, the dual-tariff customs plan, the splitting up of goods and services – would influence the political declaration in such a way as to keep the backstop at bay, avoid a hard border in Ireland, and allow the UK to say it can have an independent trade policy.
That is why her reaction in Salzburg was so furious.
At a stroke, it seemed that Donald Tusk and Emmanuel Macron had pulled down that elaborate and fragile aspiration.
It may be for that reason that London appears to be introducing a harder conditionality: we won’t sign up to the backstop unless what is in the political declaration is to our liking.
UK sources say this was always implicit in the negotiations, and point to Theresa May’s letter to Donald Tusk on 19 March.
This was the letter in which she re-committed to agreeing a backstop, something she had to do or else the EU would not have agreed to a two-year transition post March 2019.
In the letter the Prime Minister argues that a future "close partnership" would mean the backstop would "not [be] required".
If that did not work, then "specific solutions" would be sought – taken to mean technology, trusted trader schemes etc.
Then Theresa May writes: "I am committed to agreeing in the Withdrawal Agreement operational legal text for at least the so-called ‘backstop option’ set out in the Joint Report, in parallel with discussions of these other scenarios."
This is where the negotiations could become brutal.
The EU is highly unlikely to accept that a "parallel" process is the same as conditionality.
As far as Dublin is concerned, Theresa May committed to a backstop in December and then in March, and it was not predicated on London getting the political declaration it liked.
The other hurdle is that London is still objecting to any customs controls along the Irish Sea, as well as any notion that Northern Ireland be part of the EU customs territory.
This puts the UK firmly at odds with Dublin and Brussels.
The Task Force is adamant that, to avoid a hard border, Northern Ireland will have to remain part of the custom union.
As we have seen, Michel Barnier has told member states any customs and regulatory checks along the Irish Sea could be kept to a minimum.
At the dinner in Salzburg, Theresa May rejected this idea out of hand.
The next morning at the bilateral meeting, Irish officials registered their unhappiness at this summary dismissal, especially since London had not waited to see the proposals being formally tabled by the Task Force.
"[Barnier] has bought quite far into this idea that whatever way we write this up it can’t be described as a border along the Irish Sea," says an Irish source. "So he’s moved further than what they’re giving him credit for. The difficulty is that they’re drawing increasingly hard new red lines.
"They’ve now turned the potentially different customs rules between Great Britain and Northern Ireland into a constitutional non-starter. That’s a political choice, not a matter of constitutional law."
However, Downing Street believes that it was necessary to lay down a red line that Northern Ireland could not be in a separate customs territory, even if controls were kept to a minimum.
The rationale is that a straightforward rejection ahead of a formal proposal from Mr Barnier would avoid any tactical miscalculation later.
Theresa May has promised to bring forward her own new proposals, most likely after the party conference.
All the indications are that they will repeat the demand that any backstop in the Withdrawal Agreement is UK-wide, and not Northern Ireland-specific.
The EU has resisted this notion for three reasons: the time left available, the fact that the Joint Report is supposed to be Northern Ireland-specific, and the fear that the UK would use the Irish issue to get an arrangement on customs and trade through the back door, and not through the future trade negotiation.
"The first point that the EU make," says a well-placed source, "is that this was designed specifically with Ireland in mind. It cannot be simply transposed like that. The risks to the Single Market would be way too high. We think they’re manageable and containable when you’re talking about Northern Ireland, but not for the whole of the UK."
These, then, are where the divisions lie.
The substance of those differences are made more perilous by the question of timing – and not just whether October or November are the true deadlines.
Downing Street would prefer Michel Barnier's "de-dramatisation" proposals to be coordinated with Theresa May’s new proposals, on the basis that any unilateral publication by either side could – in the current climate – trigger instant acrimony and poison the well before the detail is digested.
The Irish Government, and the Task Force, simply want the UK’s new ideas to be put forward as soon as possible.
At the same time, if proposals are leaked, then the process is also damaged.
Normally, three weeks before a European Council, EU ambassadors in Brussels meet to receive a first draft text.
Then they meet a second time, then there is a meeting of "sherpas", the personal advisors of each of the prime ministers.
"This time around," says one EU diplomat, "there’s not enough time. Also, normally any draft you put on the table seems to be flying around in all kinds of directions in the European quarter and on the streets.
"That’s going to be one of the key challenges in the next weeks: how can we manage this communication-wise, while at the same time get to a solution that we all feel collectively that we own."