well, since it seems I'm the only one who has ever done the exact swap your wanting to do, here's how I did mine.
Allright, first off, the C6 fits rather nice in the tranny well.
The tranny crossmember that held the 4R70W, works perfect.
I didn't have to change anything there.
I also reused the stock shifter and cable.
The one main thing I had to change was the length of the drive shaft. The C6 is longer then the 4R70W. I had to get roughly 5 inches cut off the driveshaft. It cost me around $80 dollars to get it cut and rebalanced.(this was the 2 piece OEM shaft BTW). I also had to use a larger yoke in the rear of the tranny. The yoke from the 4R70W was too small. Since I took the motor and tranny from a donor vehicle, I had everything I needed.
I also had to run new tranny cooler lines.
Also, your factory speedo won't work(unless someone knows how to make it work by a cable driven speedo).
I think thats about it, if you have any other specific questions, lemme know.
May you fly low and fast
rest in peace JL