Let me just note, I want to discuss these things because of the very Catholic discussions I have read on other fora (HMiS discussing with Gladius, John Lane and the Robert Bellarmine forum, etc.) I do not believe it is a dogma to hold the we do not have a Pope. It is quite a difficult thing to say, actually.
I do, however, have a question: do the majority of sedes hold that the new priestly ordinations are invalid?
Most of your questions to the sede's would be better posed in the Crisis section since Sede's are allowed to speak their minds in that subforum and only in that subforum.
This is an SSPX forum that allows other Trads to join with us.
Most of us in the SSPX and the non-dogmatic sede's aswell would also agree with you that it is not dogmatic whether or not the Pope is a true Pope.
We await a declaration from a future Pope and/or Council to say so.
In the meantime, knowing that what they are preaching is contarary to the faith we disobey them as is neccessary for our salvation.
To answer your immediate question, even the SSPX doubts the new ordinations and when a NO Priest realizes the errors of the V2 Anti-Church and asks to join the SSPX he is conditionally ordianed(The condition of course being that he was not legitamately ordained already in the first place, since one can only be given Holy Orders once, same with Baptism, if someone doubts the validity of their baptism for some reason SSPX will conditionally baptise them)
Hope that Helps and Welcome to the forums.