Somewhere I've written about an article I saw in Omni magazine one time about "how to have a mystical experience." Part of it had to do with depriving yourself of sleep, which probably works, if by mystical experience you just mean an altered consciousness.
I don't have any raging techniques to mention, anything surefire. But it seems like normal seeking, persistent, normal, relational prayer and devotion -- over the long term -- making it as personal and up close as possible, would be your best bet.
Putting aside mystical experiences, I wanted to say something about "The Point Of No Return," which is a title I'm putting on an experience I've had over the years, going back maybe 12-14 years, that doesn't happen very often. This experience is tricky to describe, like describing a dream. But it has always occurred when working with putting things in a series, or working with the things in a series that is going out of order in some way.
Like, say, you have 12 cards and you need to put them in order. Like alphabetical order, numerical order, in order by the personalities on them, something like that. At some point you may get these two sensations: 1) Doing it is vain or there could've been an easier way; 2) You're at the point of no return; you may as well keep going no matter how vain it is. I guess the sensation comes -- and I haven't had it for years -- quite at random. I tried to invoke it a few times intentionally but couldn't.
It really could be that whatever the spark for deja vu is might be in operation during this series work, and something about the point of no return just flips it for a second. It's brain work, after all, and brains like the harmony of a series, but sometime feel stymied by whatever.