Yes, it's interesting that your game theory approach is formally similar to what I'm saying here. I'm sure someone else said roughly the same thing centuries ago. Feuerbach was close to it.
For me, the driving force here is irony. What would be the most ironic result when it comes to religion? For religious statements to turn out to be true after all, but perfectly mundane in that the truth was hiding in plain sight all along. Irony is the guide to profound truth in this case. But for you the guiding light is evolution or something like that.
I'm not sure the "mapping relations" are the same in both hypotheses. Again, you'd be mapping theology to something pretty abstract and unheard of, as far as most religious people are concerned. I think, then, you'd be reducing theology to game theory. But I'm mapping theology to earthly experience, so I'm positing subliminal contents that likely register at some unconscious level with religious believers themselves. I'm not just reducing their theology to a lower-level theory.