In Streetpass Mansion / Monster Manor, I have made some dumb decisions that have made it basically impossible to progress. On the other hand, I am enjoying several of the others and wouldn't want to lose my progress in those games. Is there a way to delete the one without also removing the others?
Yes. By going into the StreetPass settings > Other Options > Delete [game] Progress this will delete the progress of selected game (without affecting the progress of the other games)
Confirmed through personal experience by deleting the progress of a game (and even deleting the game itself) and other StreetPass games' progress remains unaffected.