That's well-argued and intriguing. I had a weird experience just on cannabis so I have an inkling of what you're talking about (the apparent breakthrough of the strange into the mundane).
I think it's a little farfetched, though, to ask for "verification" of the supernatural. Indeed, there will always be doubts about miracles, as there are doubts even about mundane reality. Descartes pointed out that we can't even be certain about the existence of an external world. So of course we're going to be able to doubt claims about the supernatural. That leads to Hume's point against miracle claims: mundane explanations will always be less subject to doubt, if only because we're necessarily more familiar with them.
What, then, is a deity who wants to reveal himself supposed to do to overcome the mechanics of belief formation?
One thing I've been exploring, though, is the pantheistic re-enchantment of nature thesis. It's possible that the mundane world is already weird and miraculous enough. So instead of thinking of breakthrough experiences as being unusual, we might adjust our perspective to see all of nature as self-developed art.
I should have an article coming out today on pantheism. Here are some other relevant ones.
