Infinite Activated Ability, Stack and Priority Question

Apologies if some variant of this question already exists, but I’m having trouble finding a relevant solution.

The combo in question here involves the ‘infinite’ life gain interaction between Famished Paladin and Resplendent Mentor.

The board state:
I had Famished Paladin on my battlefield (no summoning sickness) and it became my turn. Untap, upkeep, draw. I tap the 5 mana required to cast Resplendent Mentor. It resolves. With RM on my battlefield “white creatures I control get ‘tap: gain one life’” Famished Paladin’s (white creature) ability reads “FP does not untap during your untap step. Whenever you gain life, untap FP. Typically when I get this combo out and there is no response I tap FP, gain a life, untap and repeat a defined, arbitrary amount of times.

The issue:
After Resplendent Mentor resolved, my buddy played an instant stating “destroy target creature” targeting my Resplendent Mentor. We both understand that I am able to respond to this at instant speed with Famished Paladin’s activated ability, tapping it, gaining a life and untapping it. However we had a disagreement on whether I could repeat this over and over with his spell on the stack before it resolves and kills my engine.

Our resolution:
After some debate it was decided that I could respond one time, putting my activated ability on the stack as response, gaining 1 life, untapping as a triggered ability and then his spell would resolve, breaking my engine.

What is the the proper use of the stack and priority? Am I allowed to cycle priority and crank my engine many times before his ‘destroy’ spell resolves even though resolution of my ability is required for untap and re-activate?

I understand that he probably could have reacted to Resplendent mentor on the stack by destroying my Famished Paladin but he let it resolve before playing his instant. Any help or knowledge pertaining to the stack/priority is much appreciated, thanks in advance.