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It sounds like a cracked flexplate or a shot torque tube bearing/coupler. I get the impression that C6 flexplates aren't known to fail so it's more likely the torque tube. Have a look in the inspection hole while it's idling.
The above, or could be the coupling plate bolts loose, where the back of the torque tube bolts into the torque converter.
Hence bolts 9 are tighten before the torque tube rear bell is mated up to the front of the trans, then bolts 11 are loctited and then installed/ hand tighted to begin with to pull the flex plate against the TC, then tighten up to spec through the access channel as the drive line is being spun to put each at bottom of the channel in the end.
If you find that its a problem with bolts 9 being loose, you can remove bolts 11 to push the plate 69~11 forward to get to bolts 9, then pull it back to reinstall bolts 11 in the end.
Here is another video looking inside the inspection hole access. Also a few pictures that I snapped. It looks like I have oil leaking around the rear main area and now have residue inside the bell housing. This was not there last time I looked inside.
Engine side, with either coupling bolts loose (47), coupling falling apart (46), or torque tube bearing going south (51).
To pull the torque tube (to get to the above parts) trans and diff need to be pulled with TT connected to them out the bottom of the car, then you can separate the TT from the trans, to rebuilt the TT.
Looked for loose bolts or nuts in the areas Dano suggested, but didn't really find anything wrong. It would be very difficult to see anything wrong until you start to disassemble the TT, in my opinion. Started prep'ing the removal of all components and got pretty far even though I was going slow so I don't break more than I need to fix right now. So in addition to rebuilding the TT, I have to fix the leaking rear main and the fuel sending units. My fuel gauge hasn't been working well for almost a year now. Going to use the upgraded rear engine plate and rear main seal. Any advice is greatly appreciated.