I agree with all that, and I think how the two major parties respond is worth looking at further.
The Tories made zero attempt at a campaign. They knew they wouldn't gain a single floating voter, and they now know how many of their supporters they have lost over the failure to deliver Brexit. This is their worst result ever, and the Party will be dead if they don't do something. However, what are the individual MPs willing to do? Most of them are Remainers. May's deal wasn't even Brexit, and they failed to get that through. If they push anything more remain, like for a second referendum, then they are all out of a job. And with a FPTP GE, I do mean quite possibly all of them. Take Windsor & Maidenhead - 33% Brexit, 31% LD, 13% Con. The Tories did not come top in a single council area, not one out of 371 so far declared. It boils down to what each current Conservative MP has lined up after the next GE. If they have a nice job, they'll stick with being Remainers.
Labour have suffered a serious defeat. They have a fundamental problem in that most of their MPs are Remainers also, but Corbyn is anti-EU. Can they get rid of him? The commies like McDonnell would love to, and they can convince themselves that they'd keep almost all their support. They wouldn't, but they can convince themselves of anything. Labour MPs, by and large, won't have anything as cushy as the Tory MPs lined up if they get kicked out, so a lot boils down to what will keep each MP in office at a GE. Take a look at the detailed council results.
https://www.bbc.com/news/uk-politics-48 ... ting-story
Outside London, only about 8 council areas had Labour in first place, and mostly only by a couple of percent. Some MPs will convince themselves they can win the LD voters back if they go full Remain. Personally, I think they're barking, but it's what they think that matters. But, most will have to back Corbyn if they want to keep their jobs. Corbyn wants a GE, and he can practically taste it. The last thing he's going to do is change Labour's official (non) position before the GE is called. He will continue to ensure the Government can do nothing effective, and call for No Confidence votes whenever there's a chance. What appears in their election manifesto is another question, as is whether Labour win it. And even if they don't, having the Tories destroyed will be a win. Remember that Corbyn is playing a long game. He hasn't changed his views (or his trousers) for 40 years.