The sound I have heard from a hot Z trans like this is under very little load at low RPM in a low gear, i.e. maintaining 10 mph in 2nd gear, barely on the gas, etc. If you actually step on the gas, you don't hear it. I think the best guess I've heard is that it's the input shaft bearings, which is why it does it more when hot vs. cold, and I think a small amount of it is normal (I've heard multiple Z's do it.)
If you're really hearing it chug away like a Model T when you step on the gas and you're not lugging the engine hard, you might have a trans that's on the worse end of tolerances, I suppose. It could also be knock. Or, it could be clutch/flywheel chatter. It's really tough to say.
You never noticed this with your previous trans, I take it? If that's the case, I would take a wild-*** guess and say your new trans input shaft is way on the loose end. Sounds like the tech didn't like the sound of it, so hopefully you get a better replacement trans?
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