I see no posts by Exxon that he has determined that EVERY wire associated with the O2, MAT, CTS, MAP, TPS, and Engine speed sensors, as well as the sensors are good. All of these sensors are used by the ECU to control injector pulse width. He should remove every ground connection, clean and reinstall. He should insure the MAP sensors vacuum line is perfect; IE: put a hand-operated vacuum pump on the tube going to the MAP from the throttle body, and insure the MAP will hold a vacuum--indefinitely.
I cannot over emphasise the importance of ensuring every one of the above listed components, and there associated circuits be tested with a DVM for both proper reference voltages and conductivity. The ECM ASSUMES these circuits are operating correctly, especially proper fuel pump pressure.
One bad/intermittent ground, or high resistance short in any one of the wires running to the ECU can cause all sorts of hard to interpret shenanigans.
It appears you have a scanner--that's invaluable in determining if the ECU is seeing the same thing you will see as you test each sensor.
As for your symptoms, you say the ECU attains closed loop status, then as you watch the scanner, the O2 signal drops to a steady .12v, followed by a ST learn of 0 count. In order for the ECU to go into closed loop in the first place, the O2 signal must have been correct, while in open loop. Meaning, to get into closed loop at the end of the warm up mode, the CTS and MAT signals had to indicate adequate engine temp (~160*), and the O2 signal had to have been constantly varying between ~.5v and 4.5v (my educated guess)--but clearly had to be crossing the center threshold of 2.5v. But, as soon as it goes into closed loop, and the ECU takes over, the system starts dumping too much fuel (injector pulse width too long). So what happens when in closed loop that doesn't happen at the transition point of to going into closed loop? The ECU now controls injector pulse width using all of the same sensors it used to get into closed loop, in the first place. So what's different? CTS or MAT malfunction as they continue to sense higher and higher temps? Wires shorting due to increased temps past "closed Loop" temps? Remember, the temp sensors act like the carburetor choke of "old". Incorrect readings can easily affect richer running.
From my reading, the Renix ECU operates very similar to the OBD-I systems, right down to saving at least some faults; a proper scanner is required to see these. The main difference that I see at the moment, is the difference in the types of O2 scanners used for the Renix system, versus post Renix Chrysler, and most other cars. The Renix O2 sensor is a variable resistor, varying its resistance based on sensed oxygen levels, versus the more common O2 sensors, that generate a voltage based on sensed O2 levels. The measured output of the Renix O2 sensor should be between 0 and 5 volts. Stoichiometric (14.7:1 fuel ratio) is represented by 2.5v. The more standard O2 sensors generate a voltage between 0 and 1v, with a stoichiometric value of .45v. Other than those differences, the ECUs use the same, or very similar scheme to control injector pulse width.
With regard to the O2 heater. The heater is controlled by the ECU, which energizes the relay until the ECU senses (??)adequate exhaust flow to insure proper operation. I interpret this to mean that some where above fast idle--2000+ RPM?--the ECU turns off the )2 heater.