Thanks k7e9 for the page number.
So Priests really get an advantage after all, only their prayer would resolve in the End of turn phase.
Or one could rule that the End of turn phase and the Beginning of turn phase are just for metagame maintenance and not actual in-story action. That will be my ruling. Only in the middle of one's turn, let's call it the Action and manoeuvres phase, can Actions and manoeuvres be used. Simple, clean, does what it says it does.
So to put it plainly, in the End of turn phase the Priest Player puts a Favour token on his Order card.
Next turn, when the Action and manoeuvres phase kicks in, the active Prayer instantly takes the Favour point and resolves, if it has enough Favour.
That brings us almost exactly to where Kartigan was, but feels easier to remember for me. When rules are well streamlined and concepts clear, it makes for easier memorization. Beginning and End are metagame, Action and manoeuvre is where everything comes to life.