I was more talking about the TH400 dinosaur pushing the LS1 round a bit, like they do to 308's in HJ-HZ. The TH400 is really a big block or truck box. What torque converter did you end up using? Something with a bit of stall so the LS1 can get up and moving?
I agree of not using the 4L60 or 4L60E boxes, but the later 4L65E from tonner and crewman is pretty good. This is why I'd use the 4L80E or 6L80E. The 4L80E is a 4spd version of the 3L80 which is simply a TH400 (this is what a TH400 was called once GM powertrain was formed, TH700 became 4L60, TH400 became 3L80 etc).