This is probably the most unhelpful notice in Edinburgh, there's really not enough room for two bikes to pass if they're both pushing. All it does is allow self-righteous people to get pissed off.
The sensible and polite thing to do is obviously to stop and pull right in to the railings letting the other person pass on the canal side.
I've had lot of self-righteous people get pissed off at me and at least I pull over (but I can't look down - makes me feel queasy) .... have they not got better things to get pissed off at?!!!
The reason I originally started cycling over as I found that it gave me something to concentrate on rather than looking down. As long as you slow down at the blind corners at the start and end, I have no problem with it.
I've never pushed and I've never had anyone complain, either I stop, or they stop and appropriate thanks are exchanged.