The cylinder head was outsourced to yamaha for further developement. This measure ensured that the 1jz would flow the kind of air needed to make 280HP. Some speculate the 1jz cylinder head actually outflows the 2jz.
In 1989 the supra went through a series of changes, front end changed, tail lights, and the cross-member changed to allow for the addition of the 1jz into the engine bay.
Many MKIII supra owners find swapping out there 7m for 1jz's
to be a rewarding swap because of the instant large HP gains
One thing to remember is that Pre 89 supra owners will have a difficult time mounting the 1jz because of the diffrent cross-member so to say the headache randy from www.bicperformance.com has created pre 89 motor mounts for the 1jz so you wont need to change cross memebers. i myself have used these in my swap and they worked wonderful.
U.S model supras never recieved the 1jz.special models in japan did though,the toyta soarer recieved it and a few others.
Good luck finding parts for your 1JZ-GTE at your local shop.
bring a 1jz in for a routine oil change and see what happens