97 Buick Park Ave chattering when stopped

1997
Buick
Park Avenue Ultra
3.8 Supercharged
160,000

My Park Ave has been developing a chattering noise when the car is in gear and I am stopped. It is intermittent and sounds like it may either be transmission or relating to the supercharger. It makes no noise when the engine is cold, but after fifteen minutes of driving it will appear. When I come to a stop with the car in gear, it makes a sound similar to edging into the rumble strips on the side of some roads. Once any amount of throttle is applied, the sound disappears completely. Shifting into neutral or park will also terminate the noise if I am stopped. As far as I can tell, the transmission is solid and makes gear changes with no problems. I bought the car used with 117,000 and have not had the transmission fluid or supercharger oil replaced. I had planned on doing that in December or January. The supercharger belt snapped two years ago due to a seized front pulley and I was forced to run the car without the belt for a few months until I could make arrangements to get that fixed. Any pointers would be great.
It sounds like a heat shield, bracket or something is loose and is vibrating with engine. The motor mounts may be getting a little hardened and transferring more vibration than usual.

Have someone put it in gear with their foot on the brake and look around under the hood to see if you can track down the source of the noise..............
I'm with Sidom on the heat shield being likely. Small spot welds just give out. If so I've had good luck if the shields are still good at using pure stainless steel worm clamps and just snug them (prop just one right now) a pretty permanent fix for that.

Trick - car off and cold - tap on tailpipe with a rubber hammer and that should surface the noise if exhaust part related,