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... huh. Something's loose for sure. you don't hear it any other time, like when switching gears or free revving?
my knee-jerk reaction is the flywheel but that's just a guess. could be the accessory system. could be the timing chain (does the lt1/lt4 have any stretch issues here? I'm an OHC guy so this is a new one to me).
Prepare for an expensive fix if it's out of warranty. That sounds like an issue in the torque tube. My car made a similar noise on shut off. The rubber coupler was destroyed. We replaced the driveshaft instead of the whole torque tube, but dealerships will only replace the entire torque tube which will cost at minimum a few grand.