The Camaro 5 forum is generally the best source for info on the AY6 as well as some of the Holden car forums. It's a rarity in the CTS for sure, the manual was offered more in the gen 1 AFAIK, they had a sport model that came with it as well as the V.
Possibly the throwout bearing?
The biggest issue the transmission has is the dual mass flywheel and crappy clutch. You can go with a RAM, Monster or Spec and convert it to a single mass flywheel. I think the RAM is the cheapest option, but they're all still intensely expensive. Anything Camaro 3.6 will fit our cars.
You have a few options I know of:
Spec:
https://www.summitracing.com/int/parts/sxc-sc36a-2/overview/year/2010/make/chevrolet/model/camaro
https://www.summitracing.com/int/parts/sxc-sc363h-2/overview/?rrec=true - stage 2, I think it goes up to stage 5
No throwout bearing with this I belive
RAM:
Free Shipping - RAM Force 9.5 Dual Disc Clutch Kits with qualifying orders of $99. Shop Clutch Kits at Summit Racing.
www.summitracing.com
https://www.summitracing.com/int/parts/ram-78180/overview/year/2010/make/chevrolet/model/camaro
They're definitely not giving this crap away, but it converts it to a billet single mass flywheel which is a wonderful thing compared to the DMF.
Running Royal Purple will calm things down a bit as well so keep that in mind.