I have similar problem and want the IS300 diff to get better ratios.
Depends on what year the car is as to how easy it is.
Early ones likne mine (99 model) needs the complete IS300 diff cradle swapped over as well.
Later IS200's had a common cradle for both IS200/IS300 models. Just find what...
You can still use the original crossmember.
I re-drilled the rubber bush mount holes on the Getrag box itself.
The back set fit nicely between the original holes, the front set are in front of the holes.
Simply bolt the bush to the crossmember and not to the gearbox, fit the gearbox and use...
Yes, you have to keep the 1G ECU in place so that the multiplex and air-con still work. I had to share several signals with both ECU's to keep all things working like a factory install.
IS300 comes with 2JZ - not the 2JZGTE.
I have done a similar conversion but in an IS200 - same car but the standard engine was a 2 litre 6 cylinder. Now fitted with a 1JZGTE VVTi engine (the 2.5 baby brother of the 2JZGTE). Similar power but not as much torque.
Drive the IS200 as my daily drive now - it is fun to drive.
Other issues you may need to look at are the suspension as the engine change upsets the balance of the car - I now have Koni's on and that has restored the nimbleness again.
The diff is an issue - not real strong. If you can find...
The J160 is not a Getrag box - it is an Aisin box. The 1G-FE is a strain for it normally. The torque of the 1UZ would rip it apart in about 5 mins of full power.
I fitted a Getrag V160 to my IS200 with 1JZ VVTi motor. Fitting the box requires some slight surgery to the tunnel as well as mods...
If you want a stand alone computer use Autronic SM2 (I have a base map for 1UZ), but if you run the standard Toyota ECU you can piggy back an Autronic SMC to modify the fule and ignition timings.