I agree with you that any "god" cannot be placed in a tidy box (which, unfortunately, is exactly what many of people of faith try to do). The enormity is beyond human brain power. Snippets, perhaps. A bit of "stardust" here and there, but as a whole? Nope.
The supernatural is an odd horse in the game. I've experienced ghosts and hauntings but certainly cannot prove them and won't say my personal experience means they are real. That's hubris.
NDEs while often spoken of in spiritual terms have real physical sources.
visions? People have had dramatically specific futuristic dreams, and perhaps they tapped into some kind of wave in the pool of the collective unconscious.
Instincts? I know 8 times out of 10 who is calling before I get to the phone. I dream about someone and know to call them because something is awry. These things happen, but I am not they are supernatural as much as being connected to others.

