First of all, thank you so much for posting this. I've been contemplating composing a similar post for a while now but haven't because I did not feel like my experience was sufficiently extensive or my understanding was sufficiently deep. I eagerly anticipate future posts.

That said, I'm a bit puzzled by your framing of this domain as "arational." Rationality, at least as LW has been using the word, refers to the art of obtaining true beliefs and making good decisions, not following any particular method. Your attitude and behavior with regard to your "mystical" experiences seems far more rational than both the hasty enthusiasm and reflexive dismissal that are more common. Most of what my brain does might as well be magic to me. The suggestion that ideas spoken to you by glowing spirit animals should be evaluated in much the same way as ideas that arise in less fantastic (though often no less mysterious) ways seems quite plausible and worthy of investigation. You seem to have done a good job at keeping your eye on the ball by focusing on the usefulness of these experiences without accepting poorly thought out explanations of their origins.

It may be the case that we have the normative, mathematical description of what rationality looks like down really well, but that doesn't mean we have a good handle on how best to approximate this using a human brain. My guess is that we've only scratched the surface. Peak or "mystical" experiences, much like AI and meta-ethics, seem to be a domain in which human reasoning fails more reliably than average. Applying the techniques of X-Rationality to this domain with the assumption that all of reality can be understood and integrated into a coherent model seems like a fun and potentially lucrative endeavor.

So now, in traditional LW style, I shall begin my own contribution with a quibble and then share some related thoughts:

Many of them come from spiritual, religious or occult sources, and it can be a little tricky to tease apart the techniques from the metaphysical beliefs (the best case, perhaps, is the Buddhist system, which holds (roughly) that the unenlightened mind can't truly understand reality anyway, so you'd best just shut up and meditate).

As far as I understand it, the Buddhist claim is that the unenlightened mind fails to understand the nature of one particular aspect of reality: it's own experience of the world and relationship to it. One important goal of what is typically called "insight meditation" seems to be to cause people to really grok that the map is not the territory when it comes to the category of "self." What follows is my own, very tentative, model of "enlightenment":

By striving to dissect your momentary experience in greater and greater detail, the process by which certain experiences are labeled "self" and others "not-self" becomes apparent. It also becomes apparent that the creation of this sense of a separate self is at least partially responsible for the rejection of or "flinching away" from certain aspects of your sensory experience and that this is one of the primary causes of suffering (which seems to be something like "mental conflict"). My understanding of "enlightenment" is as the final elimination (rather than just suppression) of this tendency to "shoot the messenger." This possibility is extremely intriguing to me because it seems like it should eliminate not only suffering but what might be the single most important source of "wireheading" behaviors in humans. People who claim to have achieved it say it's about as difficult as getting an M.D. Seems worthy of investigation.

Rather than go on and on here, I think it's about time I organized my experience and research into a top-level post.