We aren't into the time period prescribed by the treaty yet because we have not invoked Article 50 (yet)
I'm not sure whether Europe is just behaving like a jilted lover or trying to take advantage of the fact that the UK political system is in turmoil at the moment but they do need to back off and let us sort out our end. No-one expected this result and it has rocked the boat rather a lot.
My main worry is that there will be a General Election - not unreasonable as there is the potential for new leaders of both Labour and the Tories and the view of Parliament - where most MPs favour Remain - is at odds with the views of the people.
The problem is that Labour are unelectable, certainly with Corbyn as leader and probably with anyone who might replace him and I am a little worried that UKIP could step into that void. BoJo as PM is one thing but Farage is quite another. FWIW I don't think it would come to that but the prospect is alarming.
The other problem is that they appear to be unmoveable on the free movement thing which might make negotiations difficult. Whatever you feel about the outpouring of sentiment over the issue it is clear that unless those that voted Leave can see a clear policy in place that will reduce the attractiveness of the UK to economic migrants from the poorer parts of Europe the electorate will get even more angry. Perhaps we could allow free movement of labour without free movement of people - i.e can come if you have already fixed up a job, perhaps if we allow free movement of people but no benefits, I don't know.
I agree with all you wrote.
I think Juncker's demands (suggestions, I suppose these days) are unreasonable... I know Cameron has gotten a lot of criticism for stepping down but I think he did the right thing. It would be difficult to spearhead an initiative you don't agree with. A "cooling off period" is a very wise thing - so that people don't react emotionally and instead act in the best interests of the people they represent.
I think it's fair that the EU wants to bundle free access to the market with free movement... I think it's a foolish thing that they be linked, but since they are, to separate them out would undermine the authority and "raison d'etre" of the EU, so I don't blame them for saying their linkage is non-negotiable. The EU says they won't budge on this, but I don't think much negotiation has taken place yet (other than in the tabloids).
I am positive that a deal can be worked out - both sides have plenty to lose and plenty to gain from a sweetheart trade deal, but I think the trick will probably be in coming up with something that both sides can sell to their electorate as a "win", while respecting the need to make a deal. The UK is in a unique position. Geographically and logistically, they are the gateway to Europe. They also share a common language with the largest/wealthiest economy in the world. I am sure there's things they could devise/implement which would be a huge boon to UK trade. One example off the top of my head would be reducing/eliminating the outrageous aircraft landing fees which would siphon off traffic from Charles De Gaulle, Schiphol and Madrid. They could also dramatically reduce or eliminate import fees for shipments from the Americas. They should be able to negotiate a better rate to export stuff from the UK to the EU than the rate that's paid by countries in the Americas to the EU. Then the UK could eliminate or drastically cut tariffs to import into the UK - and suddenly the UK would be *the* go-to place and conduit for all companies in the Americas who wish to do business in the EU. They could do the same with red-tape and laws/paperwork regarding manufacturing. If they can negotiate a better tariff from UK->EU than other countries have, and they can reduce the burden of operating in the UK, then they could see a resurgence of manufacturing - just like how Honda, Toyota and other manufacturers have been opening plants in the USA rather than shipping from Japan.
In short, the UK leadership needs to analyze what the differences are between the UK and EU, then leverage those differences to create a business-friendly environment. If they can do that, they could experience an economic boom that would be unprecedented. However, I fear that political infighting and power-mongering will stymie such intiatives. I'm a British citizen myself and I live there about half the year, and with all due respect to my fellow Brits and to my homeland, one of the big problems in the UK is the hatred towards those who are successful and the fact that most Brits (in my experience) would rather make sure nobody else is getting something they aren't getting, even if it causes them economic harm. So sweetheart trade deals will be criticized by the opposition as being designed for big-business and to help the rich, the same with the other ideas I had above - and most of the things the UK should do probably can't be done, because everyone will want to make sure they downvote and block anything that might funnel money into the pockets of someone whose already wealthy.