My answers would be that we're arguing over statistical noise.

I take what I consider to be the simplest explanation in the absence of a credible alternative, that prayer does nothing when the recipient is unaware of it.

I take that view because I've never heard an alternative explaination that didn't appear to break the second law of thermodynamics.

extraordinary claims require extraordinary evidence.

A magical, invisible, omnipresent, omnipotent "all known laws of nature defying"-being that answers prayers, requires significantly more evidence than a small effect in some meta study.

Absolutely. My point is that "I'm an atheist so I'll take the option that agrees with my personal beliefs" isn't a valid line of reasoning. You could symmetrically argue "I'm a catholic so I'll take the option that suggests there is an effect, albeit a small one". Now we're just arguing whose personal beliefs are right.

A more properly scientific line of reasoning would be to instead say that you'll assume the small-to-nonexistent effect is nonexistent until somebody produces a model capable of predicting the proposed small effect, or a myriad other arguments along the same general lines.