This is a conclusion of exactly what you said: we use j/p only to define the position of the Rational/Irrational functions, changing each of them (N for S, T for F - what's called "Internal/External") makes no difference in j/p.
The point is that you can make the rest of the dichotomies work under a function paradigm by introducing certain other notions to the function model: +/-, Limiting/Empowering, Valued/Unvalued (if you hadn't already) and Strong/Weak.

You need to move beyond this rigid conception of functions where the possibility that there might be some property you haven't identified yet is excluded off hand.