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.
Here's some more realistic numbers-
> The survey by polling firm YouGov showed that if a referendum were held immediately, 46 percent would vote to remain, 39 percent would vote to leave, and the rest either did not know, would not vote, or refused to answer the question.
https://www.cnbc.com/2019/01/06/britons-would-now-vote-to-st...
Here's an aggregate of polls that show much stronger support for "stay" than "leave":
https://whatukthinks.org/eu/questions/if-a-second-eu-referen...
2. Why do you expect that the vote will turn out any different? One third of the country wants a hard brexit, one third wants a soft brexit, and one third wants no brexit. There is no way to make even a majority happy. Having another vote will put you right back where you were two years ago.