So after some communication with Hypex, the thought of one of their guys is that it is a grounding issue in the 2-channel Chassis.
While I was careful to perform every step the same across all five channels, it certainly is a possibility that I borked something along the way: I would be a fool to not think that a possibility.
After a press of work gets cleared, I will try a few different things to see if I can identify what is happening. The easy one is to unplug the external inputs from the XLR connections and see if the Amps still make the unwanted sounds (this is the primary step Hypex asked me to take next and if I follow they want to eliminate something outside of the Female Chassis Mount XLR Connector being responsible for the noise; so powered on while connected to Speakers with no cable connecting to input).
The other thing I will likely do if that test still results in noise is to switch amp modules from the 2-CH to the 3-CH Chassis as this will absolutely answer whether it is a bad module or a bad build.
If the latter, I may just need to scrap the current XLRs in the 2-CH Chassis for new ones and start that process over again...
...Somehow, my biggest concern is that I will need to redo the XLR connections and whatnot in the 2-CH Chassis and not that the two modules are bad. (While it is absolutely possible one or both could be bad, it just really doesn't seem all that likely that I got two lemons and they just happened to both end up in the same Chassis... Yes it is within the realm of possibility, but much less probable than anything I would place a bet on.
)
It's looking like by Wednesday I can sit down and start playing Amp doctor. *fingers crossed