I got my JP at, or just a hair above, 1mm... which is pretty close to 1/32 of an inch.
I just played with everything: saddles, bridge height (lowering the bridge by a few 10ths of a millimeter made all the difference) and truss rod. I get a little buzz here and there, but nothing you can hear through the amp. I get no chokes on high E bends.
But, every neck is different. Have you straightened out the neck to nearly flat with the truss rod? Leaving too much relief in a low action setup can cause a "valley" that begins to rise after the 12th fret. This can cause buzzing and fret-out in the upper registers.
I have some relief in mine, but not much. I just eyeball relief instead of measuring it... fretting the 1st fret and 24th and tapping with my left hand pinky, or right hand index towards the middle of the string to see how much clearance is there.
I would recommend getting the neck nearly flat, with just a tad of relief and THEN re-do your setup and action adjustments (if you have more relief in the neck than necessary right now, you might actually have to
raise the action a tad to get back to where you want to be)... This might just solve your issue.

Good luck!
Ryan