IIRC (its been a while) the O2 sensor should show an AVERAGE value of about .450v, but if it is working correctly the value with fluctuate very quickly over a range of roughly .250v and .650v, give or take. If the value is steady, or too far to one end of the spectrum or the other, the O2 sensor is shot.

Problem could also be leaky fuel injector(s), bad temperature sensor, or thermo-time switch (if your motor has one - I can't remember).

What most mechanics would do under your circumstances is to swap your box with another unit to see if the same symptoms persist. Getting another box may be a problem.

Another approach is to tee a volt meter into the oxygen sensor leads to see if fuel starvation is a problem and under what circumstances. You need not concern yourself with precision values, merely the gross abscence of fuel under your test conditions.

Lastly, take the car to a Bosch BSC and have them do a diagnosis of computer and system performance. While a BMW dealer may be reluctant to mess with it, a BSC would probably work with you. Remember, all you want is diagnostics, not repair.