OK, guys. It IS the catalytic converter, but it is NOT shot, only loose in it's housing. My dealer showed me a tinkly one off another Crossfire, and said it's a German problem, also afflicting Mercs and Audis.
He said, "it's thousands to replace", and I replied, "how many thousands?" He said he'd let me know.
So I drove off to a surf beach to catch some waves, 1.5 hrs each way, thinking over and over that God would know exactly where and how and with what to pinch the steel casing to grip the platinum converter inside it.
Well of course God can always exceed a mortal's aspiration, and He doesn't need help. Back home the noise was gone, and is still gone two weeks on.
The dealer got back to me with $NZ2804 (=$US1450), and I told him I'd think about it. I have faith that I will never have to fix it.
Best Regards, Jim in New Zealand.