rather than about falsity of related arguments

E.g., you could check whether there's anything of pragmatic relevance in ideas like the convertibility of transcendentals. Just ditching convertibility of transcendentals can easily imply a God that is not similar to the God of e.g. Aquinas, to a lesser extent Aristotle, to a lesser extent Leibniz. This doesn't take much time and quickly rules out large portions of the "God" conceptspace. (Also, people who believe in vague "God"s (e.g. "God isn't a person, God is the Goodness inherent in the structure of the universe") are forced to refine their concepts; of course, most people think of God ideologically and so the questions most immediately relevant to them would be more sociological than metaphysical, for better or worse.)

(Presumably I disagree with Vladimir_Nesov about the value of thinking about the problem in such terms in the first place; I can only argue that most folks aren't decision theorists and so must grasp at morality and eternity in other ways, and that I am on the side of epistemic humility.)