Here is an 88 Supra with a Chevy 5.3L motor.
http://www.cardomain.com/ride/1668435
Wow- my car made another forum. That was a lot of work, but was a great learning experience. I've also put the 5.3L into an RX7 and am putting one into a BMW E34.
A few words about motors & costs:
99.9% of car guys do not know about the all aluminum L33 Gen 3 truck motor. It was introduced in 2005 model Silverado SS and GMC Sierra trucks as the "high output" motor. It is rated at 310 HP/330 TQ. The points about the LS1 are correct, no one wants to sell them for anything close to a reasonable cost, and they usually have well over 100K on them.
I bought the iron block Supra motor complete for $400 from a local junkyard.
I bought the aluminum L33 motor for the RX7 for $800, and the second L33 for the BMW for $850. I was able to sell parts off of the motors to offset the cost of replacement parts such as intakes, oil pans, etc. This motor will accept all Gen 3 parts such as heads, cams, etc. for performance mods.
I'm not here to fuel a pissing contest about which motor is better Chevy vs. Toyota. I think it may be availability, since the Toyota/Lexus motors and performance parts are harder to find at a decent price here than the Chevy ones. In my case it was also standardization, since I knew I was going to build other cars using that motor & computer system.
As to the original topic, and also as noted above, the Supra mounts are different starting in '89. My parts donor car was a '91 and my swap car was an '88, so I found out about this firsthand.
What I did was use some LS series conversion plates from Carshop Inc. These allow Gen 1 SBC mounts to bolt to the Gen 3 engine. Mike from Jags That Run made some thicker aluminum spacers for me like what he uses for the Datsun Z-car swap (did I mention I have one of those with an LT1?). I cut & bolted some 1/4 steel plates to the motor mounts on the car, and used some older Chevy motor mounts (again from the JTR Datsun swap) between these and the aluminum spacers.
My motor sits too high since when I did this I used a truck oil pan to mock up the mounts. I used a Camaro pan for the install, and it allows the motor to sit lower in the car.