Interesting. I'm INFJ and I know tons of INFJs who have the same problem: insomnia. I like how you attribute it to the fact that it is because our brains won't STFU.
I go through a similar phase: 3 or 4 nights with a few hours sleep, pass out on the 5th night. I can usually make the 5th night come sooner by trying out some sleep techniques, but those only work one night, and I'm always back in the cycle. And besides, Ive exhausted the suggestions out there for insomnia anyway.
Have you tried some wine or alcohol (just a little) before sleeping? It seems to help for me. This is kinda weird, but I fall asleep better when I sleep over/crash at a friend's place or at a hotel while traveling. I think it's because there are fewer things my brain/mind associates with my surroundings, and there are fewer things I can start bouncing my thoughts off of. It's hard to explain, but when I sleep in a new place, there's less existing thoughts/emotions tied to the place.
Edit: I work out a lot, too... the thing is when I work out, I feel mentally/emoitionally healthy, but it still doesnt have an impact in helping me sleep, it gets me more energized! (to not sleep lol)