Adam I don't know if this is possible or not.....
I haven't read all posts about this so sorry if I'm suggesting sth that's already mentioned.......
But can you in any way disconnect all or most of the modules and see if there is no humming, and then connect one at a time at least in order to see which module that causes the issue.
If it goes away when you only have one or two modules connected then at least the backplane is OK?
Anyways... good luck with this thing, bl¤%¤# h¤%¤%¤ this must be annoying....