Were there any remnents of the Old West by 1930? In any case, going back too far in time would put the next Red Dead in that cliche time period of "Shootin' Injuns" and looking for gold in them thar hills. The American Revolution or Civil War could be interesting for missions, and I'm sure Rockstar would do something much more original than previous Western games, but the typical natives and gold-hunting are very old.
The addition of Cthulhu improves everything. Seriously, try to think of any movie, game or book that wouldn't benefit from our dark master. Cthulhu Fhtagn!