LlBr

AFAIK, These engines are also a cacophonous mess when innocently idling (especially cold). The only time they sound fantastic is when they're hot and winding up or down at high revs.

Alfaguy2

Could be a simple problem with the exhaust. A loose or cracked mounting bracket etc. I have this problem with my TR6 - tried to cure it a few times without success.

The engine jerks when turned off which can shunt the exhaust against another surface causing a noise. The exhaust can cause the noise to reverberate making its location or cause difficult to locate.

fpb111

Porsche has been addressing this drive train rattle in the flat six engine cars for some time. In the early 911s that I have owned, 1969, 70,72, (78 with spring center replacement disk) one could hear the trans rattle very clearly at idle after warm-up.
In the SC they tried rubber centered clutch disks. this helped to dampen the rattle until your clutch rubber disintegrated and the disk had to be replaced. The trick was/is to replace the rubber centered disk with a spring centered one and live with the rattle.
I have not been in a 996 with a lightweight flywheel but I bet elimination of the dual mass flywheel would sound very much like replacing the SC rubber centered disk with a spring centered one, louder trans rattle at idle and warm shutdown then the dual mass flywheel has.