One important thing is not symmetrical in your analogy: for scientists, the truth is approximated by coming up with hypothesis, making experiments and then observing the evidence. If the evidence, as collected by multiple experimenters, is strong for the hypothesis, then that hypothesis is accepted, otherwise it is rejected. Anyone with enough skill and equipment can reproduce the results. If someone can't, the results lose weight and more research is needed.
In your subjective personal experience, nearly all of this is missing. You only have a hypothesis: there's a God that is causing this personal experience. There's no experiment we can make, as you say yourself, that would convince us that you do feel something magical, and that that feeling is coming from something supernatural, not from your brain (which is known to be prone to illusions and hallucinations).
Even if I felt such experience, I would be convinced that it was a brain illusion and I don't know of anything that could be used to convince me otherwise, except perhaps something real, tangible (say, God tells me what black matter is in a way that I could not have possibly come up with by my own means, or explains why he doesn't just show up and tell everyone he's real, or give me some power to alter reality and prove to everyone I've met Him!).
There's no symmetry here at all.