Well what I normally do is pick a couple of clans that people can play, for example having a Lion Daimyo and her Dragon husband, and 2 clans that no-one can play like a crane daimyo and his crab wife.
I do however allow people to play the other clans but I ask that people have at least one dis/advantage that links them to the 2 base clans for the game, whether that be a blissful betrothal or as a hostage, just something that provides a reason why they would be willing to work with them.
This does limit player options but it does create a much more cohesive group of characters that should be willing to work together, as well as giving a defined set of clans that can be antagonists without causing game ending issues.
Also the current version is very big on Samurai drama, and I was lucky in that my players gave me a lost brother, a wife, a lover. As such the big bads in my game were the Brother who was a mahotsuki who had corrupted the other characters wife and the thirds lover. My players are loving even though there was much wailing when the crane had to duel his lover and behead him to prevent him rising as a zombie.