Well what ever odd gremlin your have, it seems to be playing its games at idle, based on your live O2 sensor data. I guess you are down to maybe looking for a vacuum leak or cracked manifold.
I forget, is it running lean or rich at idle? You mentioned that you ruled out leaking fuel injectors because it does it running on LPG fuel as well, but does the gas fuel pump run while it is running on LPG? If the fuel pump is still running, injectors, or the fuel pressure regulator can still leak fuel into the intake.
Edit: OK I rescanned the entire discussion here. The PCM says it is running to lean (at some point in time, when, at idle or cruise, we do not know yet). The O2 sensor says it is running rich at idle, very rich, but normal (not lean or rich) at cruise. Rich at idle sounds like too much fuel to me since you seem to have ruled out the O2 sensor and sensor circuit as OK.
Hopefully your scanner will arrive soon and get you live PCM data soon!!!! This one is a real puzzle! It may be wiring to the PCM or the PCM itself?
I am wondering if one them is wrong, the O2 sensor or the PCM, or of both are right, how that can be? If the PCM is getting a signal loss in the wiring from the O2 sensor, rich could look normal to the PCM, and normal could look lean to the PCM! I think?
I am not an engine guru, but have you check all the plugs, checked their condition for any signs of mechanical issue like valves?