I can see some comedian out there getting ready to tell you: Noise? Filter it out! just hang a 100 microfarad capacitor across each audio input!

Call Rotel and raise hell. It is entirely unreasonable to have to connect a separate ground cable between an RS232 controller and the device it's controlling. If that were necessary, they would provide a pin for it in the cable. Actually, there IS a ground wire in the cable, so what the heck?

But also check for parallel runs of anything near anything that could be inducing that noise.

What happens if you ground the switcher to the RP6 but not to the receiver? This makes no sense but you should try it.

Does any of this noise show up as artifacts on the screen? What happens if the screen is off, or better yet not connected? Does the screen have a three-prong power plug? And, of course, its media box? Maybe if you ground the RP6 to the TV media box instead of to the Rotel....