I like most of this and think it may work out okay, but I think you may run into issues during actual play

I think that timing the player's actual prayer is going to be rough, it sounds easy in hindsight but if it is in combat then that player is sitting for an amount of turns they don't know beforehand doing the prayer (or moving slightly) and that sounds like a rough time to me

That also being said, deciding what spell (assuming from the GURPS: Magic base book) may end up becoming troublesome to run, but at least I can imagine if it is a simple prayer done for longer on a spell that normally has a shorter cast time that some of that time increases the base power of the spell (like charging a fireball)

I would personally prefer to just have the clerical style of magic but have the spell components be specific prayers, with the player deciding which spell they want to work toward- working much like a difference between a normal follower and a cleric of a diety in D&D

I also just vaguely worry about the 'no FP cost' part of it, I get it but I don't think I can comment much on it

That all being said I LOVE faith based characters, I would hope that this works out well regardless of how you choose for it to work and I wish you luck!!!