I think that is a good idea, as long as the voting is all done at the same time. By the way, you don't need 3 - Deal means May's, No Deal means WTO.
The choice of three options is also fair, but it would have to be written in that the winning margin couldn't be - for example - 34, 33, 32; the winning vote would have to be a clear % ahead of the next most popular, or it's No Decision and would have to be rerun. If the rerun was also No Decision, then lord knows what would happen next, it would have to go to a penalty shoot out...