I would add an additional ground between the engine ground for the ECM (there is only one ground on the RJM harness) to a new body ground location. It should connect directly to the same stud or bolt on the engine that the ring terminal ground on the RJM harness uses. It may not help, but it is an easy way to alleviate the most likely ground issue.
The second thing I would do is check the continuity (resistance) between the metal case of the O2 sensors and the RJM harness ground, just to make sure they are 0 Ohms. The A9L is a 3-wire. One for the 02 sensor signal voltage, and two for the heater. Sensor ground reference is the exhaust itself. The factory harness has a separate 02 Sensor ground from the computer to the exhaust, but the RJM likely ties it together with the single ground. Also disconnecting the O2 sensors would be an easy test also.
The engine doesn't need to warm up to go into closed loop. Heated O2 sensors can start performing after only 60-90 seconds. I think the real issue that you are likely facing is that when the ECT sensor reaches a certain level, the adaptive functions will be enabled. On the A9L, adaptives are less than ideal and can cause some real headaches at idle. If you can datalog the sensors, I would look at the O2 sensors, the MAF voltage, and the TPS. Even a 10% variance can cause the adaptives to really jump the fuel around and cause stumbling idle. If there are issues, I prefer just to disable adaptive below 1500. If the TPS voltage is off slightly, and the ECM thinks it is above idle that can also make adaptive worse.