I'm not sure that would work. If you phase-invert one of the channels and then subtract it from the other one aren't you just going to double the amplitude of the bit you're trying to get rid of? ie you've got a point on the waveform which has a value of 0.3 (we won't worry about units they're irrelevant) if you invert this you get -0.3. If you take this away from the corresponding 0.3 on the other channel you'll get 0.3 - -0.3 = 0.6
It's getting too late for all this brainwork (it's 02:25 here) I'm off to bed. Hopefully someone will have figured it out by the time I wake up. Then we'll all say how obvious it is .