The 4l60e in there is a very solid transmission. But like any automatic, it NEEDS A COOLER.
Put a good external cooler on it, a hydraulic filter, and reprogram the shiftpoints to stiffen everything up, and you'll have a tranny that will hold 600hp without a problem.
Weak point of the FBodies (3rd and 4th gen)?
7.5" 10 bolt. He *WILL* destroy it once he gets traction. The pinion crush collar squishes under hard launches, and it will get to the point that the pinion gear will 'walk' up the ring gear on an especially hard launch, and split the case. You can weld the tubes, put a Ratech solid pinion spacer in there, and use Summit's rear stud girdle, but you're still playing on borrowed time with the LS1's torque, and the Fbody's 3-link suspension.