DC power from speaker amp for power to switch relays?
No, you cannot drive relays with audio outputs, in any case they will switch weirdly when high power sound is send to them, back to normal when sound is quiet. All this assuming you don't blow up anything.

I really don't know much of high end audio equipment to give more info about this.

The best solution for this scenario I could do myself is some micro controller listening to A and B channels and switching the relays to the last output which generates an audio signal.