Try bumping it back to 60 (or even 50 or 40!), and try that out. It might be really grueling--difficult (perhaps more difficult in some ways than at 120) and boring--but concentrated practice at these tempos will eventually make playing things at performance tempo more fun and relaxed. You can approach it like a Zen meditative thing, to hone your concentration."Slow motion exercises" - sounds great! I've started with 120, which is close the actual tempo of the song. I was always going to wind back the nome before cranking it because there's a couple of fills I play to that rhythm where I tend to speed up a tad and I obviously want it them to be cleaner.
As a self taught player I have an uneven skillset with plenty of gaps (most of which I have no intention of filling) so I find that on the rare occasions where take a "pick and stick" and practice instead of play, it not only improves that particular rhythm, it also helps tidy up related areas of my skillset that were a bit half-baked in unexpected ways.
It should be so easy but I've tended to have a hard time committing to actual practice as opposed to playing songs and fudging the difficult parts. Should be saving it for jams and gigs ...
Kaufman's slow motioon exercises are designed to be practiced at quarter note = 54, I think.