Claw -- I agree. TPS isn't a formal group, in fact, there's at least two, if not three various 'groups' of TPS holders. And there are, to my knowledge, other TPS holders not represented at all. These groups are ad-hoc, not formally recognized in the sense that they were not established by the court or the UST.
Now, while the TPS folks can vote however they feel, they really - in my current understanding - do much other than pitch a fit, and file appeals {which may be equitably moot}
So I concur with your comment that effectively whatever befalls P's befalls TPS -- and the EC is the one that's negotiating on behalf of P/K Preferreds and Q commons.
...Catz
.... Please, just call me Catz ;) - - - - - {and the requisite, all IMHO, do your own due diligence, and make your own investments}