John, to return to sacramental theology, I'm sure you'd agree that if the form, the matter and the intention are present, all else to the contrary notwithstanding, the sacrament is valid.
For even a pagan can baptize, as you've noted, and as St.Thomas says, a heretical priest validly confect the Eucharist, their erroneous or heretical conceptions of what constitutes the form or even whether they believe in a form notwithstanding so long as they intend what the Church does.
Now it is clear that the intention to consecrate, at least habitual, is present, so the argument does not prove and consequently the opinion that error as to what constitutes the essential form in the minister invalidates the sacrament is therefore without foundation.
I understand the argument drawn from the episcopacy of the Apostles or the high priesthood of Christ does not convince you, it is unlikely a dispute that has gone on for a long time will be settled and universally agreed upon just like that. For myself, though, I think they are valid for the reasons I've mentioned.