Quick update. I spoke with Fender, and they said the following:
The spec for the neck pocket depth on an American Standard Precision Bass is 0.57" (+/- .10). So a measurement of 18/32" seems pretty normal.
So it seems the spec for the AM Standard is below the normal 5/8" . Although 5/8 does fit in the spec range above, it's not the target spec. Just a heads up for anyone else going this route.
On the plus side, I went to see Green Day last night in Portland. After 26 years of listening to these folks, I finally got to see them play, and it was a killer gig. They played a massive set, were full of energy, and the sound and lighting engineers were totally on point. Mike D was killing it with his P bass and Fender Bassman combination. Now I need my P bass project to work