I don't use feeler gauges. Insert nut in slot, scribe a pencil line on the nut using a piece of .020 aluminum which conforms to the fretboard curve and have at it until I'm close, install strings and do the rest by "feel", with strings on.
My approach to nut slot depth is to consider the nut as almost a zero fret, as long as no buzz on a fairly hard plucked open string tuned to pitch it's not too low. A nut that is too high causes intonation problems by making the first two or three frets high because of the difference in height between the nut slot and top of the fret. It evens out by the fifth fret but drives some guitar players crazy when open E is in tune and F is sharp. It's quite a revelation when they finally understand.
...That's why NUT JOBS are so important.