Great advice above, especially about always being drunk when you ride!

I've been practicing japanese martial arts for many years, and in general I would say that Aikido practitioners have the best rolling fall technique, suitable for bicycle falls... Judo will condition you for harder falls and "Kara-te" means "empty hand", a style you already seem accomplished in!
Karate practitioners don't practice much fall technique either.

When going down sideways on ice, it can be wise not to let go of the handlebars... but I guess for your riding style this is mute...

I have experimented with rolling falls in the dojo wearing a helmet, and it does make the fall clumsier from a standing position. However the few times I've made rolling falls from a bicycle, the helmet didn't get in the way...

Glad you didn't hurt yourself too bad