I've been told the LSD of the Supra TT 93-98 is used to swap for the SC400. They said it bolts right on. Or you have a little more money, get the TRD LSD that's made for the Supra.
for info on compatible toyota diffs. I've got the non-turbo JZA80 Supra (SZ) diff (for auto or 5 speed manual). Bolts straight in but the final drive ratio is slightly different
TRD make a performance, clutch type (not Torsen) LSD for the '93-'98 TT Supra with A/T that should bolt into your diff housing. Talk to Curt @ Elmhurst Toyota for details and best price.