Also as a general update -- still no solution. The connections all seem to yield the appropriate power via multimeter, (I have no oscilloscope). The guy who made the case suggested removing the 5V connection from the PSU and taping it off -- none of my modules use it anyway, and the only way he was able to replicate similar interference on his end with same PSU, was with a slight negative power draw on the 5V rail. So I tried that, but it made no difference. Trying to isolate it to a particular module hasn't been fruitful either -- the sound becomes present regardless of which modules I put in, just once there is "enough" of them to (I presume) create a certain power draw level at which point this buzzing noise starts up. I got a recording of the sound today. It's amplified a bit of course, it's subtle at normal listening levels, but problematic if you try to build patches over it.
https://www.dropbox.com/s/gu3fjwnf91vlgfj/modular_sound.mp3?dl=0
Using the same modules in my Synthrotek case creates no such sound, though it is a smaller case with only 1 row (it's the case this new one was intended to replace).