Re: Looking for the best combo for WP + BP + forum
I don’t know of anyone who has integrated punBB and BP. Here’s a plugin to share logins between the two systems: http://www.rkblog.rk.edu.pl/w/p/punbb-and-wordpress-integration-plugin/. The group-level management stuff would probably have to be custom coded.
I’m not aware of anyone who has integrated a different forum software into BP that will meet your list of criteria, though maybe someone else in this forum has.