The best buzz-free action I can get on my MIM Jazz bass is about 2.4mm (a bit worse on the E string), tested with slightly harder plucking than I'd normally play with. I've *very* carefully tweaked the rod in small increments, let it sit overnight, and measured gap with a straight-edge and feeler gauges over the last couple of weeks. Even like this, there are a couple of notes where, if I pluck *hard* and let the string ring, I'll get some buzzing.
I'm guessing that you've reached the limit of your fretwork. I looked at my fretwork with a 24" straight-edge (new bass!), and could see places where here and there a couple of frets are too high or too low. I'm no expert, but it doesn't look like the MIM Fender's fretwire was pressed-in as consistently as my Ibanez when originally constructed. I guess doing the "Mexican hat dance" on the frets at the factory isn't the best way to secure them in the slots...
I was previously "eye-balling" the relief, and using the low E as a straight-edge (fretted at first/last fret). I seem to get a bit more precision with a straight-edge and feeler gauges. At about .43mm, my relief is a bit above the spec of about .3mm, but I've tweaked the rod so many times in the last couple of weeks that I want to let the neck "settle-in" a bit. This one-piece maple Jazz neck seems quite finicky compared with my 6-string Ibanez laminated "aircraft carrier" neck.
The bass plays pretty well, and I primarily got it so I'd have a simple 4-string to learn slap on. I'd prefer to get a better 5-string at some point, but if I stick with the 4, I'll probably get some pro fretwork done after the wood has settled-in for a couple of years.