You shouldn't have any problem getting the action down to .0625", (4/64), at the 12th fret. My Strat neck is right around that figure, and I did the neck/fret work on that myself.
My JM neck was worked by Cagey, and was at about .040".....
I've since brought it up to about .050" because I decided to try using a pick again after 20+ years of not using one, and I have been hitting the strings a little harder.