If we are all very lucky, Hillary Clinton starts a full scale intervention in the Syrian civil war and disposes of Assad. The local situation might calm down enough to resolve the refugee crisis, at which point many Britons will wonder why they wanted a Brexit in the first place.
Because american invasions in the Middle East are so good at "calming down" the situation. See Iraq.
Invade Libya also. And Ukraine also. There's plenty further of "stability" for Hillary to spread around Europe, to had to her handywork already in progress.
Brexit is more of a sympton of what's out of whack in UK politics than the EU.
Because the EU, as we all know, is the land of butter and honey where the stress are paved with gold. Where there is no mass youth unemployment, no ongoing ethnic conflicts, no shameless corruption with the eurocrats favoring corporate sponsors against others. Oh no, the EU is paradise, none of this could possibly be happening! It is entirely "in whack", loved by its subjects, who throw flowers in the path of every imperial deputy that deigns to leave Brussels to a visit to the provinces.
I cannot see the UK renouncing to passporting rights for financial services. The economical cost of such a power shift would be too unpredictable. If really put under pressure, I'm even convinced Theresa May would accept to keep freedom of movement if that would ensure her to keep the passporting rights.
Negotiating?

The UK can and will just break the EU and negotiate with the remaining pieces. It's only a matter of letting the pieces be in the right place before moving. That is why they're taking their time...
But would European leaders really have the capacity to grow something good out of this? That's where I'm the most sceptical.
"European leaders" will do what political leaders always do when faced with institutionally impossible decisions: preserve their power and let the institutions collapse. Not one of them actually cares about the EU, they care about their careers.
Maybe the EU parliament could be that trustee?
That joke nearly nobody even cares voting for? They're useless. Power rests with the executive branch in times of crisis, with the people who can actually give orders and have bureaucracies (and armies, btw) to follow them. The EP has nothing, they'll just be unceremoniously dumped out of their buildings and offices when the states take them over.
The EU is a "dead man walking". A dead empire walking on the inertia of fear of breaking ranks. All it takes is one good kick for all ranks to break.
Tell me, o europhiles, are you Swedes, French, Spanish, Italians, German... or are you Europeans? What are you willing to do for other European? We saw that in Greece already: threaten them into poverty less they be blocked from trading overnight, their businesses and the political system brought to collapse. Help? Hah! Threats and violence,, only so much "aid" as required to pay back the creditors from other countries.
There are no Europeans. There won't be any. There is no nation called Europe, there won't be any.