I can make it a “Catholic/SSPX Caucus” but the “Catholic Caucus” label excludes SSPX and Orthodox.
The SSPX is Catholic, just not very obedient and not very politic. But clearly validly ordained Catholic clergy. And yes, for many years an arguable ex-communication was in place, but that has been lifted.
Your position is 100% false. The previous two popes consistently held SSPX were part of the Church, and the current Pope has done nothing to change that. As well, the SSPX leadership doesn't contend that they aren't part of the Catholic Church. Whatever differences there are, neither side is making the claims you created.