Wegner LS3 bolted to ? T56?

[Rocketw19]

I have a LS3 bolted to a 6l80 (stock) I am told the 6l80 will not take the 850 HP. my thoughts instead of spending $5000 to beef up the 6l80 why not buy a new trans and sell the 6l80? I have no clue how much the T56 cost or what I will need even. I am not that smart. I will ask Casey (motor builder) and the shop thats installing but your input here is always good and welcomed. its a automatic and a street car, want to keep it that way lol
what the best cost effective or just best way for me to do this in your opinions please. will I need a new 3rd member also? I have new 3.77 gears, posi and Moser axles. so I am thinking trans and 3rd?

62 impala if that matters