I don't understand your argument against the Caucus notion as the RM has laid it out. It seems reasonable to me that a group cold self-define and discuss a topic without mentioning or derogating a group not in the self-defined group.
In practice it might be difficult in the case of some groups, but I don't see why the principle is bad or how the RM is painted into a corner.
Previously, the caucus definition was suggested, nurtured and refined to provide a hospitable zone under the theory that quibbling and contentious voices drown out the discourse of the like-minded.
The newly proposed model of the caucus (i.e., the LDS/Catholic caucus where the trinity is argued from two opposite sides) is the antithesis of a safe-haven. It's a boxing ring.
It's non-Euclidean. The parallel postulate no longer applies.