I believe I discovered about 90% of the problem. There is a 1KVA, medical grade, toroidal isolation transformer that isolates my system from the grid. Thus any line leakage to neutrals or grounds is blocked, eliminating any hum induced from leakage currents into the signal grounds. Apparently, there is some sort of oscillation problem between the Class D Marantz and the isolation transformer. Clearly, it is triggered by the music load put on the power supply which draws power from the isolation transformer. It is important to note the Marantz also has a toroidal transformer in its power supply as well. The two 200W monoblock Conrad Johnson Premier Fives, which are tubes, are not affected in any way. Neither is the solid state Parasound 2250 V2 amplifier at 275W per channel. The Parasound has a toroidal while the Premier Fives do not. But the Marantz, at 275W per channel, simply goes nuts! About 90% of the resonance problem disappeared when I plugged the Marantz directly into the wall.
I say 90% since there is still an unacceptable amount of vibration in the Marantz chassis. I ordered 4 square feet of DynaMat Extreme sound deadening material, so a thank-you to all who suggested it. I am pretty certain this will eliminate most of that 10%. It is certainly thick and heavy enough!
As for the 1KVA grid isolation toroidal, the longer-term plan is to add two 7.5 KVA isolation transformers, along with the existing 1KVA unit, and run them all from 240VAC, thus generating three independent separate derived supplies for the stereo. It appears I need to move that time frame up!. If I still have a problem, then it might be time to look at a new amplifier. I am sure there are amplifiers with better sound quality out there that will drive subwoofers quite well.