BuddyPress.org

It would require to make some kind of plugin for bbPress.

The drawback of this ends up to still be the additional query per avatar that you hit the database server with, to ask BuddyPress what each users avatar is for each visible avatar. It might be possible to hook a bbPress function and join the query together to include the extended profile table to get the avatar location, but this type of thing hasn’t been developed or released yet.