Does Bullet actually not support compound shapes for soft bodies, or is it just our code? I haven't actually found somewhere in the Bullet docs that say compound shapes cannot be used with soft bodies, but that doesn't always mean much.

There's no documentation on this, from looking at the code it seems like noone really thought about using softbodies in compounds.
Also having a compound object made out of soft bodies doesn't make sense, at least to me.
Imo this is one of the many cases where the game engine tries to support too many options that aren't really useful.