Well you can't fit the GT4 manual transmission. Its a 4WD.
Best bet would be to grab the 3SGE ST182 (?) import gearbox, this is in the JDM Celicas (and those convertibles you see here).
The 3SGTE obviously does fit, but it would be a fair bit of work. Don't expect much change from $4K minimum. Perhaps cheaply fix the SX, flog it off and put the money with that $4K and buy a real GT4?
I had some gearbox repairs done to my GT4 at Bob Romanos' and they did a very nice job. So if you are really keen on the swap, perhaps they could be good to talk to.