Hey, guys while it's not a truck, I need help with my 1983 Toyota Celica GTS, it has about 145k miles. Any help would be most appreciated

The is the issue, when the car is cold it runs great, doesn't backfire or buck. Once it starts to warm up and reaches operating temperature it starts to backfire, slightly at first, and gets progressively worse. Then it starts to lose power and start to buck/surge over certain RMPs starting at 5k then lower over time until it won't accelerate and wants to die over anything past idle. If it gets to that point turning it off then back on again will raise the RMP range but it will eventually get back to that point.

Here is the full list of everything I have checked/replaced.

EGR Cleaned and is working normally,
AFM working properly except for slightly high resistance on the closed setting,
replaced EFI coolant temp sensor,
new remanufactured injectors,
Ingntor replaced with GM HEI unit,
Coil replaced,
Fuel Filter replaced, original was in fine condition,
Fuel Pump replaced and filter cleaned,
ECM check done by the way the service manual outlines,
O2 Sensor changed,
Throttle body cleaned and TPS to factory specification,
Plenum cleaned along with inlets and EGR passage.
New Spark Plugs and Wires,
New Cap and Rotor,
Timing Set to factory specification,
Trouble codes checked and none show,

The only things left to check that come to mind is the pickup inside the distributor and fuel pressure. I also did a visual inspection inside of the ECM and it all looked ok except for the 100uf 16v capacitor has some corrosion from what I think might be leakage, but don't know if this would be causing the issue.
I did happen to catch the car on video doing something similar to it while not driving, here is the video.

 

If it leaked, even a teensy, tiny little bit, it's no longer a 100uF capacitor. I don't where it's located in the circuit, but caps like that are often part of the power supply/conditioning circuit. Thus, they affect every part of the ECU. If the power to the rest of the ECU is changed, and it is, when it compares incoming voltages, currents, and other signals to it's references, the references will be off, thus, the comparisons will be off. Thus, it's output corrections to make the engine run properly, won't be correct.

Since there's no real good way to test a cap in-circuit, if you're a good solderer, replace it If you're not, replace the ECU.
Use a low wattage soldering iron, and don't leave it on the pad of the circuit board too long. You can lift the pad. Then, if you know what you're doing, you have to reset the pad. And maybe the run.
A quick touch to the pad, if your iron is good n clean, and there's touch of flux on the pad, and the solder should flow perfectly. When you get done, the solder should be shiny, and in a small mound up the lead of the capacitor. If it's dull, or not mounded, it's a cold solder join. Suck the solder off, and try again.

Sorry, I spent my entire working life as a lead electronics technician on radar systems. I got pretty good at soldering.

Good luck to ya!
Pat☺