I wanted to follow up on this in hopes that it will help anyone else who experiences the problem. After narrowing down the issue was within the RM4 and was louder on the POST out, I contacted Bruce Egnater, who told me exactly what the problem was:
"I'm going to take a guess and say it is possible the high voltage regulator transistor may be shorted. It is a TIP50 transistor that is attached to the smaller upright heatsink on the power supply board. To check this, carefully measure the high voltage on the collector of the transistor (which also is the heatsink). Should be between 315VDC and 330VDC with the four modules installed. Measure the regulated voltage at any number of places, which is easily determined from the schematic. It should be right around 300VDC. If it measures within a couple of volts of the raw supply on the collector, the transistor is shorted and is the source of the hum. If the measurements are as stated, the problem will be elsewhere. You must do this test first to determine if it is the problem."
Sure enough, we determined that is -exactly- what the issue was. I confirmed it with Bruce and he is such a great guy - he sent me a replacement part at no cost. It was replaced today and I have confirmed the hum is gone (although I do still have to lift the ground on the RM4).
The replacement part Bruce sent was a BUL216, which is a higher voltage rating part.
If you have confirmed your RM4 has a hum that you know should not be there (and the best way might be to test it against another RM4), try having a qualified person check the stuff above. Because we narrowed directly in on the problem and saved all that time, it was less that one hour from tip to tail on getting it fixed which saved me a lot of $$$.
Bruce has created another Egnater customer for life!
Scott