Sounds like progress! The extra voltage you're seeing on the O2 sensor has to be coming from somewhere (the sensor itself cannot produce those kinds of voltage values). Plug everything in again, and when it is running badly, disconnect the heater circuit only to the O2 sensor (the two wire connector). If the car runs well and you are measuring between 0.15-0.85VDC on the sensor, you know it is bleed-over from the heater circuit into the sensor line (if you are using a digital multimeter you may have to watch it for a while to see the voltage peaks and troughs because the meter doesn't update very quickly). Replace the sensor and you should be good to go...

Good luck!