Practically speaking, kiss channel balance goodbye if you want to use bias as a 'balance' control as you've described it. By rendering channels 'unequal' in regards to signal level, all you will accomplish is the destruction of the stereo image, ie: point source imaging, depth, extension, and low level resolution. You will have the exact same issue you started with, only worse, much worse. A balance control is an attenuator, not a signal reduction.
Can I tweak L-R balance by differntial biasing?
My new (to me) Almarro integrated does not have a balance control but my room is slightly asymmetrical. I'm playing a little w speaker toe-in to try to correct this, but I just had another idea. Bias spec is 0.20 volts, with 0.18 volts suggested as a minimum which will reduce output slightly but provide more tube life. It seems to me that if I bias the output tube slightly lower on the "louder" side, it might shift the balance slightly toward the side that is biased higher. Does that make any sense???