If a far away STA can be understood by our AP (if it was on Ch 1) then I think putting this AP on Ch 2 is a bad idea. That means that the far away STA is close enough that it would cause interference with our AP which is on CH 2. In my experiments, better thoughput is achieved by having STA's / AP's on the same channel as they can arbritrate with each other, while they can't on co-located overlapping channels. I know you are a sharp guy so I hate to question the logic, but I can't think of a situation where it would be a good idea to put an AP on Ch 2 in this situation. Another point is that if there is heavy Ch 6 and Ch 11 traffic, I don't wany my AP on Ch 2 because it is of course receiving and transmitting more interference to and from our Ch 6 AP's.
Ping ---> Pong :)