I built a one-shot around this idea on a heavily-modded Tiny D6 system, letting people choose which of the 4 they wanted to be with variants like wealthy or scientific Victorian, captain or gunner pirate, disgraced or retired Samurai, cattle driver or 49'er, and so forth. I set it in San Francisco to get some good conflux of cultures.
Of my 4 players, 3 of them chose to be rich Victorians. facepalm
Diabolical. I'm thrilled by the idea of it happening to someone else.