Right, off you go. 0000000001 - test. 0000000010 - test . . . phew, only another 1022 to go.
The thing is with electronics, you always have to be thinking laterally. Just what did that fall do? Just what happened when you changed the batteries? How much of a trap can be created by two factors both effecting it at the same time?
I'm perplexed by two controllers being the only ones switched. Perhaps your man is right and the receiver's switches do control other functions and the programed code is achieved another way . . . or maybe fixed.
I certainly would start by working with the switch in the original position, and looking for something else. On the very old units, some selection was done with a punched strip clamped in a plastic block about the size of a medium sized computer chip. Sprung connections were made through the holes.