So I did some detective work today. The game plan.
1. Remove serpentine belt
2. Remove supercharger belt
3. Replace serpentine belt
4. Start engine
5. Monitor on start and stop, check for same noise.
6. Remove serpentine belt
7. Replace supercharger belt
8. Replace serpentine belt
9 Monitor on start and stop, check for same noise.
1,2,3,5,6,7,8 sucked. Our engine bay has minimal room for big forearms, bought me a nice tool though. I was able to get away with using a breaker bar and a socket for tensions but not with this car. 20 Bucks later got me a nice tool from Hazard Fart (harbor freight).
The car running without serpentine belt exhibited no strage sounds on shut off. However you will notice that the pulley spins, it shouldn't spin when the clutch is not engaged. On the last check with the belt off the pulley does not spin. The car when started for the first time with the belt and stopping doesn't make the sound but after subsequent stops it makes that sound. Leads me to believe the PCM is fine and the clutch is bad.
I had a fun day of wrenching on the car. Serpentine belts suck and the proper tool will save you a lot of time. I may get a new pulley and start from there. Also awaiting feedback from my friend who is the Tech down at the dealership and see what he says. But it is isolated to the supercharger, that much can be confirmed.