Watching it again on my CRT in a more awake state, I've decided to do another pass, this time at 576p24 instead of 480p24. I've scrubbed through and re-done all the work I did at 480p, and the results look pretty much exactly the same on my computer this time (not sure why 480p looked better last time I tried it).
Tomorrow, I'm going to go through shot-by-shot again, with the 576p version, and fix anything I missed in my first pass. Then I'll render it out to a 720x576, 23.976fps ProRes file, convert that down to 480p, and make a new DVD and see if that looks better.