The left side of the pocket is cut flat while the right side has a bump to the far right. I measured from the bottom of the pocket to the top of the fingerboard and the right side sits 1/64" to 2/64" higher. Should I fix this before installing a new nut?
As a layman i'd guess the uneven pocket is either a slight factory flaw or a conscious compensation for the overall intonation, given that the intonation was adequate with your previous nut.
Compare the original nut to a new one to determine if the latter had been compensated for with some kind of indentation, or the likes (implying factory flaw). If so, you could then even out the nut pocket to fit the new replacement nut (I'm assuming you want to replace the nut).
If you still feel uncertain, probably double check with someone who really knows guitar tech (i'm stating the obvious, i know).
In many types of repair, sage advice from professionals is to work on the least expensive part. In my opinion, that applies here too. My advice would be to install the replacement nut and slot it according to its installed height. (A pencil lead laid across the last couple frets can trace a "limit" line for you on the face of the nut.) Your replacement nut will certainly have more than 2/64" excess material -- probably much more.
Seriously, though, if you screw up the nut, you're out $20 or so before you get to try again. Alternatively, if you screw up the neck, it is considerably more. Work on the cheapest part.