Sounds like a cool idea, but I would say not a good idea in my opinion.
You'll have to change out the front springs to big block springs due to the additional weight. Then the car will be nose heavy compared to the small block. There are a couple big block C3's around my area and the owners say they don't handle as well as a small block car.
I believe you'll have to upgrade the radiator as well. Then you'll have to get Corvette specific water pump and drive accessories for the 396.
I don't know if you have a auto or manual transmission. If its a race engine with a radical cam, you'll need a stall converter for a automatic and maybe have the transmission freshened up to handle the extra power. If you have a manual transmission, you'll probably have to put a fresh clutch/pressure plate in. Make sure your u-joints are in good shape to.
That's all I can think of for now. I know Joel and kstyer will add a bunch of "pitfalls" to be aware of.
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GEN III 5.7L "LS6" Engine swap
TKO500 5 spd.
3.54 Dana 44