07 silverado tranny upgrade...

So i have had my silverado new body style for about two years now. I have the 5.3l with tow package that came with the LSD rear end and four speed. I have a race trailer and would like to upgrade my tranny. I know i can get the hd cooler but i need a better converter and would like to pick peoples brains about the right way of handling my objective here? The truck's powerplant mind, has the 5.3 that is turbo charged with a t76 that seems to be just amazing with HP tuners. So now i just need some advice as to where i get started? Thanks...