Engine stalls when idle on longer trips on 1990 Chevrolet Celebrity

On longer trips (greater than an hour drive), and seemingly worse on hot days, my car has been pretty consistently getting into a state where it stalls when I stop at a red light. It takes a few tries, but it eventually starts afterward.

None of the check engine, voltage, or temperature lights have come on prior to any of these events.

I noticed if I give it gas, or pulse the break in a certain way I can sometimes keep it from stalling out.

I had it in the shop to check the idle air intake, and they said it was clean. Also they were unable to reproduce the issue in the shop, though it has been happening on most stops after a certain point on a long trip.

Note: This is actually a 1988 model Celebrity.

You may have a problem with a sticking torque converter clutch solenoid in the transmission of your 1988 Chevrolet Celebrity. Let me give you a couple of symptoms specific to a stuck TCC solenoid. After extended driving (at least 15-20 minutes) at speeds over 45 mph, when you come to a stop the engine will die. The engine will restart OK but die again as soon as the transmission is put in drive. After a few minutes (in most cases about 20) everything will begin working normally. If this matches the symptoms you are having then chances are the TCC solenoid is sticking, which keeps the torque converter clutch applied when coming to a stop. With the TCC locked there is no slippage and the engine cannot idle. The repair would be to replace the TCC solenoid and servicing the transmission (filter and fluid).
Yes this sounds very much like what is happening. I forgot to mention that when I try to restart the car, the engine starts fine, but fails when I shift into gear. That matches what you are describing.
You might also have a timing problem.