Sounds like an old standard problem. I just can't recall what
the other teams said the issue was.

Check the various electrical wires under the hood that go to ground. Especially in the harness -> ecu area. It sounds like it could have gone into "limp home" mode. (not sure if Toyota has that) Many manufacturers run the car EXTREMEMLY rich when this happens. Notice any milage problems?
Is the header glowing when you get home?

Sounds like it could also be:
-clogged fuel filter or lines.(or bad petrol)
-Catalyst has broken up and is plugging exhaust port
-problems with ide stableizer system being buggered up.
running far too lean after warmup (called the ?? IIC air valve?
on the supra)

Interesting that someone mentioned Cartalk. Here's an old
common Supra problem: http://cartalk.cars.com/Columns/Archive/1996/December/14.html

Ed
-used to be a rally mechanic
-supercomputer repairman