May's deal strongly implied some sort of strong customs arrangement. It was what she was negotiating for and was the idea of the whole UK backstop - that if the EU wouldn't agree any deal that let NI leave the EU customs union then the whole UK should stay in some sort of arrangement - which also kept a lot of industry happy. And would involve a lot of continuing regulatory alignment between the UK and the EU. Basically as close to membership as May could get without accepting Freedom of Movement.
As far as I can see it, and everything May said and did from her speech at the 2016 party conference onwards was pretty much consistent with this, her two principles were dumping freedom of movement and being able to do independent trade deals. She was after the closest future arrangement she could get that allowed both of those - hence the Chequers deal, and the various shades of customs agreement she tried to get.
My reading of the post referendum polling (unreliable because most people are very unsure about hypothetical polls so you get loads of "don't knows") is that most people wanted to get rid of freedom of movement. A large minority of remain voters included. I think it was about 60-65%. But similar numbers also wanted to keep Single Market access. When polled about choosing one or t'other there was a decent majority for keeping FoM and staying in the Single Market. So even though May didn't see that, had there been a big move from remainer types to coalesce round that as a compromise, more moderate leavers like Johnson and Gove (and large chunks of the Conservative party) would be happy - as would quite a lot of moderate remainers (i.e. most of the rest of Tories and quite a lot of Labour).
The problem was that with Brexit faltering a large number of politicians on the remain side decided to go all out for the win, and having a second bite of the referendum cherry. This destroyed May's premiership - and her deal was so shit that it polarised opinion still further. Rather than Brexiteers mostly saying, "oh well it's too hard" a bunch decided that if no acceptable terms for leaving were on offer - then we should go the whole hog and hard no-deal Brexit. Hence a tiny group of MPs (the ERG and the "Spartans"), with fewer than 60-70 people would have been the only ones getting what they wanted. And make no mistake, no-deal Brexit was looking increasingly likely - by miscalculation rather than design - but we couldn't keep going on extending the deadline - yet not even voting the hold a second referendum so that was always going to take 9 months to organise, which was too long for an extension.
Whereas if enough soft Brexit and remain MPs had voted for full Single Market access in the indicative votes - then May might have gone off and negotiated that. Which would be much easier to do.
People went for the high risk winner-takes-all approach. On both sides obviously, as that was clearly what Johnson was going for with his divisive tactics as PM - and May's deal could have got through with the ERG hard-Brexiteer types too. But I think that's why this Parliament deserved to be put out of our misery.
Personally I don't think remaining in the EU is a viable option, after voting to leave it. Not unless there's massive changes, which there's no appetite for. The Brexit Party wouldn't go away, and some future Conservative government in 5-10 years time could just win and take us out, citing the unfulfilled referendum result. There's a good chance of another major Eurozone crisis in the next recession, or the one after - the structural problems of the Euro have barely been touched. And there'd be an awful lot of betrayed Brexit voters complaining about every minor foible of the EU. Hard Brexit will entrench a small (ish) group of very unhappy remain voters too - though I suspect there's fewer of them, at least a third of voters have wanted to leave the EU since the 70s (though I think numbers dipped in the mid-80s) - Single Market membership with some policies to address the issues created by freedom of movement could have been a nice sweet spot that upset everyone the least.
Johnson's deal will be a less close relationship (a direct consequence of the choices made by remain campaigners) - Labour winning would be highly unpredictable. They want us to join the Customs Union but have co-decision or veto over EU trade policy - something Norway, Switzerland and Turkey haven't been allowed. I can't see them getting very much, then who knows how their second referendum would go, when they came back with May's deal again, with a slightly reformed backstop.