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I had Jim at Automaster's in Bowling Green replace mine with a new 4L60e. I am in the process of rehabing an abused 99 vert, and it had some sort of shift kit that would make you cringe when it shifted into second gear. He charged me about $2300 after core charge. Don't know what it would cost to switch from manual to auto.
Not sure about the C-5's but on the C-6, the bellhousing on the rear of the engine is different for the two transmissions. Shifter, center console changes, software/firmware changes to the PCM and who knows what else.
It's a lot of work to swap out and a lot of money to have someone else do it.
I'm starting my swap in a couple weeks. Pulling out the Z06 drivetrain, and installing a built auto.
Pedals, shifter, everything from the back of the engine to the diff has to come out and be replaced. And then there's the wiring harness that has to be changed. And a bracket fabled up for the shifter cable.
And then get the PCM tuned for your application.
If you only want an auto trans in your car, you'll be much better off selling yours and buying one with an auto. If you're really attached to your current car, plan on $6000 or so. And that is with used parts...