I have a requirement to be able to rotate screw or nut in increments of one degree. This is for optical alignment purposes, although it could be nice for torquing accurate preloads as well.
I like Mikes suggestion, we use lots (well, quite a few) 1/4-80 or 1/4-100 or similar fine pitches for our fine adjustment. You're currently at about 32 TPI. Having used 4-40's for fine adjustment on one part while possible, it's not super easy.