Yes the TT swap is possible. that being said, here is my advice:
1. compression test, if it checks out, a complete rebuild might not be neccisary. the 2jz-ge thats in it is very strong, and i would suggest looking into some turbo kits for it. The motor is VERY capable of 20+ psi, and under that can be held reliably. Along with the kit, you'll need the other odds and ends, exaust, bigger brakes, injectors...etc. The TT swap would be well over 10 grand, and the turbo kit can keep you well under 10 grand, and over 400 hp. (easily)