So, it caused a schism.
You're absolutely correct (except UGLE formed in 1813.)Bro Mark,
Regularity comes in several levels and forms. It's a gray scale or floating point. In comparison recognition is yes/no digital. Being not recognized does *not* automatically mean being clandestine. This description makes PHO sound regular in almost every way but a decision on how many levels of sovereignty there should be. The divide between the Antients and Moderns was no larger than that and they unified into the UGLE in 1817.
Might PHO reconcile at some point? In several countries there are both national and state GLs that get along and that could eventually happen in the US. If they have a definite lineage it's possible. If that's the only point of departure on regularity.