On opening it up it was really obvious what was causing the hum. There are 4 large capacitors on the top (CPU) board, that provide smoothing for all the lower voltage DC supplies. A couple of these were obviously bulging. So I whipped all four out and replaced them with 2200µf 25V 105˚ Panasonic electrolytics. While I was there I replaced a bunch of the smaller caps nearby.
This is a real bear to get to, being underneath the CPU board. In order to get the transport out you have to first open the tray and unclip the oval NAD bit on the front. Then retract the tray again, open the cover, remove the CPU board, and it's pretty obvious.
The transport is an ATAPI/IDE one, made by Raymedia (RMC) part number RL-A700. This is common to a lot of CD, DVD, and SACD players of the period.
Cleaning didn't help. The supplies were tested good, and this transport really has nothing to adjust, so I next ordered a replacement pickup. Part number for the pickup is SF-HD60.
This made a really big improvement, but it still stalls very occasionally and 2 or 3% of the discs I've tried today don't read. After repeating the clean, relube, reassemble, test cycle a couple of times, including pulling the spindle motor and giving that a bit of a spray of iso (did I mention that it's a pain to get to the transport under the CPU board), I've decided to bite the bullet and just order a whole new transport for it.
So that's where this one is at. It actually sounds really good, and with the exception of three useless channels will make a lovely all-in-one stereo. I think I'll set it up in my office at work once it's finished.