I just had the belly pan off and while the engine was running the dogbone mount was all tight. Actually. I was wondering about the mount attachment to the frame,[where bolts are rusted] but it was solid. My belly pan is of questionable solidity where it attaches to the side panels. The damn clip on nuts are rusted, so I have added other screws. I hate taking it off.
Vibrations are transmitted. That the dogbone is tight might not remove it from consideration. I speak in regards to folks who have put on poly (or other hard) dogbone mounts and ended up removing them because of the vibrations that were transmitted through them. I suppose, however, no one likely snuck under your car and replaced the dogbone with a stiffer one
Skirts/pans can make noise but I don't think they have enough mass to transmit like you seem to be suggesting.
Anything in the belt paths (mainly serpentine belt) that might be experiencing a bit of resistance?
And, I've got to ask, manual (DMF)?