If physical world is manifestation of “supernatural higher levels”, it makes those levels natural by definition and their presence must be observable in material world. Lo and behold, that is, indeed, the case. If it were not, we could not even speculate about non-duality, because dual nature of reality would be as far as we could go. As a matter of fact, if there was supernatural outside the scope of science as you propose, the only possibility for arrangement of reality would be Deism.

It would also mean that you could never reconcile science and religion/spirituality. I would go as far as to say that if Deism were true, we would not even contemplate “the supernatural” that is detached from natural because there would be no indication that reality is arranged in such a way. That would, of course, also imply that we would have no religion/spirituality because we would have no way to infer existence of Supreme Being solely by empirical reason and observation of natural world.

In other words, if supernatural was not natural we would have no way of knowing that it exists. Thus Deism is invalid and refutes itself by its very definition (and it's why it lead to physicalism – Deism minus knowledge of God equals the situation described above). So, a slight correction – if there was supernatural as you propose it, we would be stuck with physicalism for all of human history.