Since your original post says you're using the "Ten Ways..." app note already, we need to consider subtleties. For example, that app note doesn't do a very good job covering common-mode issues.

With two hundred displays, you probably have dozens (or even hundreds) of power supplies. Are the 'grounds' on these display boards connected to a common potential? If the supplies are floating (such has most wall-warts), then the solution might be as simple as using the 'extra' 6 conductors in your CAT-5 cable as a common return.

It's fairly clear from the diagrams that this is a one-way system, so there would be no contention. But does your PC drive an 'enable' line? Unless you have fail-safe biasing on your backbone, that driver needs to always be enabled.