It's possible, hopefully someone has done it before. Otherwise your ECU is going to be looking for an A650 and throwing a fit about it.
***ALSO i just noticed your original engine is a DOHC which means you only have 1 speed sensor on the transmission, even the 4 speed 1UZ cars have 2 speed sensors on their A340 transmissions. So not only do you need to trick the ECU/TCU to modulate the shifting you're going to need to simulate a speed signal for it to see so it doesn't freak out still. Try Dakota Digital, you may be able to figure out what it wants to see in relation to the sensor your transmission has (insert MATH) and simulate the second signal to make it happy.***
OR get a 1UZ VVT-i A650 simulator for use with a maual trans except splice in the Montero Aisin TCU into the 1UZ VVT-i harness (TPS and temp) and let the stock TCU control the AW3.
OR do a NON VVT-i with a later Gen 2 (Gen 2.5) transmission, because all that stuff works happily together.
OR OR OR! Swap in an A650 because they work much better anyways.