I'm really sorry, I had forgotten the details on this. The memory of those extra pads on the PCB did float through my mind but I didn't follow up on it.
Here is a link to a thread that discusses the pads (I don't know why BYOC doesn't include this on the build instructions) -
http://www.buildyourownclone.com/board/viewtopic.php?f=12&t=32756&hilit=amp+selector+phaseYou need to add 3 resistors, a 10K and two 100K (marked 103 and 104 on the PCB, although the 104s could just as well be 10Ks), a single pole two way switch to flip the phase back and forth (the switch is wired as the centre pole to the pad labelled P on the PCB with the two throw tags to T1 and T2) and cut one PCB track (the track between P and T1 on the top side of the PCB).
This mod wires the unused half of IC2 as an inverting buffer and the extra phase switch switches the signal to the primary of T1 (secondary drives channel OUT A) between its normal configuration and an inverted version from the output of the normally unused op-amp. This is similar to one of my original suggestions except I was saying to modify the circuit of the second op-amp in channel B so that it had an inverting input with a switch between that and the non-inverting input.
The BYOC mod using the 'un-used' op-amp adds the phase inversion to channel A and not to B as you wanted but does it really matter which channel gets flipped?
By the way, following the BYOC circuit diagram is pretty tricky because the IC pin numbers on the diagram do not correspond to those on the PCB layout (sigh!).
I have now added these instructions to the BYOC mods thread.