It can be a bit loud with mallets and discussion, so I don't think one can expect a really quiet meeting to go on without a hitch. As you mentioned, privacy would best be afforded if ya'll can get into the BAPS room. However, it seems the common space is already double-booked by an event with Diane Di Prima.
I've cc'd the BAPS organizing list to sort that out.
In general, I'd be happy to host ya'll in the space, plus we generally encourage informal groups, clusters, etc, to use the space, especially consistent and in solidarity with our values, as it seems you and your group may very well be.
// Matt