It sounds like the rules are a an addition to the by-laws and are basically a guide telling you the conditions under which fly-screens are more likely to be allowed. However, unless they are incorporated as part of the by-law they have little standing (although a phrase in the by-law along the lines of the by-law being “subject to rules that the EC may decide from time to time” may cover it).
I think you are right on the money with the the idea of mediation at Fair Trading. I can just about understand the issue of the mid-bar in terms of the look of the building from the outside but it seems to be so minor and nit-picky it will be hard for them to justify in front of an independent arbitrator. You’ll find the appropriate form HERE.