Cool idea, except the pirates wouldn't be part of it cuz the era you're calling the "old west" didn't start in 1800 - westward expansion was in its early beginnings then. The classic era of gunslingers and saloons and stuff was really a very brief period between the Civil War and the 1890s. Another forgotten bit of trivia about that time is that around 25% of cowboys then were black.
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
Well, you just gotta only allow one archetype per team, figure out a system for the players to draft their choice fairly, and then let the chips fall where they may.
Or you play a system that has build a world where the age of exploration, king Arthur, the Russian revolution, the hanseatic league, the itialian city states, the spanish inquisition, and much more are all happening at the same time.
7th Sea has some wacky world building, but it stays realistic enough to be quite believable and coherent.
"Red Sun" Toshiro Mifune and Charles Bronson. After bandits steal a sword being carried to Washington, a samurai and a gunslinger must unite to bring it home.