[AnimalMuppet]

Well, nobody can be made happy, I agree. Maybe they should go for "least unhappy". Put three options on the ballot - remain, hard Brexit, and May's best deal. None of the three will get a majority. (Brexit might get a majority if you lump May's best deal and hard Brexit together, but as you point out, those aren't really the same thing.)

What do you do when nothing gets a majority? You could go with whatever gets the most votes, but as you said, that leaves the majority unhappy. Instead, on the same ballot, ask everyone what their second choice is. If nothing gets a majority of first place votes, then go with whatever got the most first and second place votes.