So you’re looking for a reason to believe that ultimate reality transcends human reason. And you’re applying the logician’s and scientist’s principle of the burden of proof to the question of whether those methods and principles are limited.
The traditional skeptic misunderstands the question of whether “God” exists. Of course, the skeptic is practically forced into that misapprehension by the religionists who take their metaphors much too seriously. It’s the mystical aspect of theism that poses the biggest challenge to atheism, since the question then becomes not whether there’s good reason to believe that Jesus rose from the dead or that the First Cause wrote specific books for us to read.
No, the question is whether existential humility (as opposed to the new atheist’s Luciferian hubris, a.k.a. methodological naturalism) compels us to be more pragmatic in selecting the myths and faith-based principles to which we inevitably resort as opposed to having rational understanding of everything.
I agree that a deity might prefer for his creatures to use their reason than to surrender to blind fear. But the fact is that the scale of the universe is terrifying and corrosive to the self-confidence of primates that might have more powerful brains than they can handle. It will take great works of art (including stories), not just scientific and technological ingenuity to enable us to cope with nature’s inhumanity. The question, then, would be whether certain religious stories are potent enough to be subjectively true, as Kierkegaard said.
I understand you consider these mere philosophical musings. But the rationalist dismissal of the existential and pragmatic aspect of religion can likewise be dismissed as scientistic. I’m not saying I’d agree with the existential or pragmatic theist, by the way. I’m just saying there’s that battlefield too.