C6's are tough and often used for racing because they are so tough. So do not be concerned about a rebuild. There are still plenty of parts available for the rebuild process. Get a reputable shop to rebuild it and it will last for many years to come. (The older guys are good with these, younger guys have not likely rebuilt any or many of these.)
The bigger issue many face is a failing vacuum regulator valve. (VRV) which is the part on your injection pump with the vacuum lines. These are end of life. There is someone who suggests he has reproduced them out there, not sure about the life expectancy. There is also one they came up with for racing that uses a cable to a valve. The cable is tied to the injection pump and moves as you apply the throttle. So converting to a stick removes this obstacle, gets you 4 gears as I recal (VS 3 in a C6), and more control of your shifting.
As mentioned above doing what you can to lower the tranny temps via a bigger trans pan and tranny cooler will extend the life the second time around. But your radiator via the built in radiator cooler does cool the tranny fluid to 190 degrees.
You may also have to adjust your VRV when you put the tranny back in. If they put a new modulator or shift kit in you will likely need to adjust the VRV to get your shift point where you want it. You loosen the adjustment screws and move it a littl towards the cab and towards the radiator, tighten and go for a ride. Continue till you get the shift point you desire.
Good luck!
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