My embryonic take on this is that there are bizarre and "mystical" experiences that people may have which can be explained using Epicurean physics in a similar fashion to the way Epicurus explained thunder and lightning and the like.
We have made incredible advances in science since Epicurus's time. In areas like weather, sensations, dreams, gravity, etc, the Greeks seem quite primitive to us. I'm suggesting that there are many areas where our knowledge is as primitive as the Greeks, one of which is "mysticism". The proper approach, to me, is to address individual mysteries with Epicurus's methodology aided by modern science. We now have advanced biology and physics; quarks, strangeness and charm, dark matter....
Discarding the unexplained as hogwash is no better than attributing it to the supernatural. Epicurus was quite good at offering multiple explanations for phenomena, while meeting his standards of intellectual rigor and avoiding dogma. And he knew when to quit, removing fear of the unexplained and moving on.