The rear axle is probably a 6.38" like ones from an AE86 SR5
but you don't have provisions for coil springs....I dunno how you are gonna fix that. The R&P ratio on the SR5 rear end is 4.1:1. It will be difficult to get LSD in that configuration if you are going to slide it around the most economical thing to do is to weld the open diff up.
If you go up to 6.7" rear end like the GT-S you'd have a wide range of LSDs available but because the dick (lol) portion is longer you will need a new driveshaft.
But once you have fabbed up a new driveshaft you'll find that the Supra 7.5" rear end will go onto the car as well, opening your options up to a lot of Hilux Hiace and Landcruiser spoolers and diffs.
Good luck they are happy cars driving a anemic Corolla makes u happy for some reason you can't put into ink....An upgraded motor only makes for instant happy motoring. I drove my friend's TE72 and I was in love...
