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Poor "Catholic Martyr" has inverted the rule of doctrinal tradition.  He doesn't accept what has been handed down as a rule of belief, rather he subjects this rule to his own arbitrary opining, thereby declaring doctors of the Church heretics and deposing Popes from their rightful throne.  It's truly a sad spectacle as he has cast out everyone from the Church but himself where he stands alone.  When he is confronted with an authority, he does not faint from asserting individual men are not infallible, implying error on the part of a great doctor.  'Tis very unfortunate that he is too blinded by pride so as not to be able to assert this of his own opinions.  So rare is this form of pride that I suspect a demon is fomenting this vice directly.    

We are dealing with the negation of a compound statement. We are talking about something that CANNOT take place without this or that. In other words we are stating the circuмstances , which are necessary to exist for this event to be incapable of taking place: the absence of only one of the two above elements, the laver of regeneration, or the desire thereof. Only one has to be missing. Things would be entirely different if the disjunction were changed to a conjunction, that is if the word "or" was switched to the word "and", OR if the "cannot be effected, without" were switched to "can be effected with". Either one of these changes would completely alter the meaning of the phrase, whereas if both changes took place, there would be no change in the meaning whatsoever.

Ah, so your handy logical analysis supercedes dogmatic tradition.  Why am I not surprised that you're not surprised that this is just now coming to light.  At any rate, all disjunctive and conjuctive propositions can be reduced to conditional propositions.  As is clear from the text, the term "or" implies that only one of the conditions is necessary to satisfy the requirements of the proposition itself.

"This translation however cannot be effected except through the laver of regeneration or its desire"

"The arrest cannot be effected except through placing him in handcuffs or filing for a warrant."

Notice the arrest can be effected in either way, so too with Justification.  Converting the proposition into a universal affirmative "can only" changes its quality, but not its meaning for it still asserts the same thing.  The idea of negating a conjunction with "neither, nor" is irrelevant as that is not the form of the proposition in question.