Something to know about this before going ham with the combos, is how this interacts with other cards, and why.
The first thing to know, which I had needed to get clarification for, is that "the order the conditions are written on the card matters", which is to say, "If A when B then C" is not the same as "When B then C if A"
Specifically, if it's written "If A when B then C" then the ability does not resolve when B happens if A is not true, meaning any effect that changes A during resolution of triggers for B is too late, whereas if it's written "When B then C if A" then A is checked at time of resolution.
So, at this point you are probably thinking "Get to the point already!", so here you go:
On the runner's turn Film Critic can host QPM first, as the runner's abilities resolve first on their turn, invalidating the access trigger, nullifying the other on access abilities.
Maya has the different trigger of "After you access a card", so it will always resolve after QPM, however, Maya can still bottom the card, even if it's no longer in R&D, so if the runner accesses it, while tagged, you add it to your score area, then Maya can add it to the bottom of R&D, assuming you havn't won off the point.
Note: I have re-written this review from it's original state, as I was incorrect about why it interacted the way it did with Casting Call, meaning I incorrectly assessed it's interaction with Film Critic, hence the first four comments saying that this is incorrect.