Perhaps your issue is that the heated O2 is doing it's job, and that when you disconnect the heater wire, the system simply goes open loop and THAT is what the problem is...something is wrong with closed loop and the engine only "sees" the problem when the sensor is heated and trying to keep the system in closed loop.
Open loop runs off of a bunch of pre-programmed/assumed values, many times if something else is going on with a sensor, vacuum leak, etc., taking most of the sensors out of the equation (again, open loop) the system runs better, or at least more consistent. I believe with the TBI setups, disconnecting the MAP sensor forces open loop, which is something you already did, and stated the engine idled better like that, correct?
Could do the same test by disconnecting (or depinning) the O2 feed wire to the ECM and leave the power wire hooked up, see if the results are the same. But again, I believe disconnecting the O2 sensor puts the setup into open loop just like disconnecting the MAP sensor (if not going into a limp mode) so you'd likely be doing the same test different ways. But at least it would prove the power wire is or is not the problem.