I do not write this to be confrontational or to simply be a jerk.. So to that end I do believe you believe your experience to be something more than our physical world can explain. I am ok with that.
I do not write this simply to be agreeable either, but I don't think there's any substantive disconnect between our definitions regarding not having an explanation, and a default paranormal hypothesis that sounds groovy, but falls short of objective examination or rationale. Hardly anything turns me off faster than somebody attempting to prove their God or some mystical wazini, or experience, to somebody else, especially me. These things if existent, need no defending, and if I want some I'll make my own thank you, I'm not in the market for whatever brand might be pitched.
Also there's room to note that experiences which challenge our ability to explain them might broadly be divided into those that involve a purely personal inner experience which apparently coincides with or reflects some outer strangeness/manifestation/coincidence, and those weird times which are more objectively placed and interpersonal, the Phoenix lights coming to mind. What my real interest is in, is in the effect they have on us in reality, a change of perspective perhaps, a quandry to peruse, a good story maybe. In the case of the purely personal, let's just say you awake from a certain dream (as an example) that was making you feel a certain way, longing, fear, lust, whatever. What's interesting to me is the way it can feel after you awake with the thing fresh in mind. While the dream no longer has an ounce of substance, the essence of it can linger as a feeling, a mysterious memory, or a desire, even though the literal order or images of the dream, have smeared or vaporized. This, I think, is the real interesting stuff- something more along the lines of a placebo affect, or an itch that you can't quite find the exact physical location of, so you just scratch around a feeling. Geez, now I'm really not making sense.
Ahem!
So in the case of intense deja vu, or prophetic dreams, crazy ass coincidences, communicating with aliens and angels with and without DMT, and etc.- I am inclined to say that even the most unexplainable and mind blowing experiences have a perfectly quantum mechanically harmonious/neurological explanation that I simply don't have the current capacity to grok. Self-reflecting, synaptic mind plays and wow stuff like that. That's cool. As I say, it's how interesting, inspiring, dissociative, decorative, or completely irrelevant apparent "unexplainable" phenomena might be in our lives that interests me personally.
Side note: I've always been fascinated by the cargo cults. The fact that these people see the planes come down with the goods, hey, that makes you and I and all Gods! It's like a free ride to Mormonville, from their perspective, based on that they've got no better explanation. Fascinating. I've been heard to mutter to myself at times, "We're all in one big cargo cult man." I mean we were a geocentric solar system back when Noory was born. Anyone who thought otherwise was wiser to keep it to themselves, until word got out, and so now we see that it's a not really a big bannana boat carrying the sungod back and forth across our sky until it's rebirth each morning 'cause Chief Stupid said so.
I enjoy the perspective checking that we do when confronted by unusual phenomena or opinions that differ from our own. I just don't appreciate boring phony self-marketing raps, and fortunately, not much of that on this forum. (In fact, this forum might be considered a positive reaction to that kind of stuff) Writing about this does inspire me toward writing a subjectively weird tale (or two) only to share the flavor of what has affected me, like the feeling that music can give you, quite explainable, but just as magical as anything in this world.
The other thing about paranormally stuff is that I really don't enjoy hearing about other people's UFO sightings and garden variety corn like that. (I posted one elsewhere here today

) Well yeah, everybody loves a well delivered ghost story and things of that nature, but what we really like is the strange and obtusely weird or disturbing turns or epiphanies. I am reminded of the memorable effects of my Nana's strange stories of old Mexico as told to us kids. I mean nobody wants to hear, "I saw a strange light in the sky..." more than a few times, but a well told tale with an edgy twist and a funky break? Perhaps a surprise or two or bumper music? That's the stuff we all miss!
One last- Anyone here familiar with Julian Jayne's "The Origin of Consciousness and the Breakdown of the Bicameral Mind"? Wordy, but a fine attempt to point out that the human association with mystica and religio/magical l history, along with schizophrenia, wraps well within a model of an evolving bicameral mind. This now largely unused bicamarilization hardware/software merger providing the necessary social order in the human tribes before the advent of conscious individualization. In Jayne's view, 90% of what we expect from Coast results from this residual, appendix-like, old brain fart. I suppose the endo-bio-pharmacological mechanics have taken the lead in this area, particularly in regards to therapeutic treatment.