CathInfo.com

The “good motives” had to be agreed to by the couple’s priest and they couldn’t use “the rhythm method” (the pre-V2 term) without permission or they would commit sin.

The “good motives” had to be agreed to by the couple’s priest and they couldn’t use “the rhythm method” (the pre-V2 term) without permission or they would commit sin.

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Yes, it was typically the sort of thing that could not be undertaken unless and except the couple's pastor approved, and at that, at least one priest argued that the morally safest scenario would include a couple already known to be especially virtuous and pious.  See Fr. Calkins (1948 ) article on the subject: https://sspx.org/en/nfp-unhappy-compromise

Why no exclusions or exceptions? Even before Pius XI couples were allowed to postpone sex to infertile periods. And Pius XII taught the same.

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There are no exclusions or exceptions to negative precepts.  Negative precepts are, as the name implies, precepts which instruct you not to do something.  The proscription against sinning against the natural law (which is what contraception is) is not something that can ever be excused from, just as it can never be excused to sodomize, etc.  The non-excluding nature of negative precepts is a very old principle, probably most popularized by Aquinas.  It is crucial to moral philosophy in general.  
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But what is crucial in the discussion over periodic continence is that it (having sterile relations) simply isn't against the natural law.  So it isn't included in the types of behaviors which would be condemned by Casti Conubii ("the pill", condoms, etc.).  The marital act itself is conducted in the natural way which is what counts for purposes of evaluating its intrinsics, and intrinsics are what Pope Pius XI is talking about in Casti Conubii.  There is no negative precept against periodic continence.  What one is being excused from in the case of periodic continence is not the negative precept against contraception, but the positive precept to procreate.  Positive precepts are distinguished from negative ones in that they command you to do something.  E.g. "go to mass on Sundays."  The nature of positive precepts is that they can, in principle, be dispensed with.  As Aquinas says, they bind always but not in all cases.  A serious enough reason can excuse someone from the duty to procreate ("be fruitful and multiply"), just as a serious enough reason can excuse someone from the duty to attend mass.
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ETA: to be clear, you have the right conclusion (i.e., that periodic continence is lawful).  It's just the way that you're getting there that doesn't work.  It's not lawful because contraception is allowed in extreme situations, it's lawful (in brief) because it isn't contraception and because the duty to procreate can, for a sufficient reason, be dispensed from.