More on this in case anyone was wondering:
The priest-paladin subclass exclusions only work for those classes and only affect each other - not themselves (that I could see anyway). You can create a subclass that "pretends" to be a paladin or a priest in part of the character code which will affect what subclass of the other type you can choose. I have not (yet) tried playing these pretend-subclasses off against one another on non-paladin/priests. If it works then it can provide some very limited control.
Pretending to be a priest whilst actually being something else may allow you call on the deity stat (or paladinorder for a pretend paladin). I have not tested for this at all but, if so, it could allow you to apply disposition bonuses/penalties to other classes. Or it may break the game...
I'll probably have more info further down the line because I may dabble a bit with this even though it is not what I was looking for. I don't think it's currently possible to do exactly what I wanted. Paladin and Priest have hardcoded components (such as the subclass string mentioned in an earlier thread relating to the Priest of Rymrgand mod).
To become a pretend Priest/Paladin simply link a new subclass of either type to the main class UUID of your choice. ("ForClassID": "UUID",). You will need to leave the subclass string alone or set it to invalid. You can also create a new order or deity disposition. And then hope it doesn't break the game somewhere (I will be testing this more).