It sounds like the system that one of our paddlers showed us back about 1992 and is used by a few manufacturers here.
It allows the rudder pedals to be adjusted without the need to adjust the rudder lines. As our own kayaks don't usually need pedal adjustment, but use that system, it means we have it right as we don't have chafe problems though the wear point is always the same.
The absolutely critical part of the path is the line needs to go round the hinge pin or round something in line with the pin so that there is no rubbing where the line goes through the hole in the pedal. It is all a matter of geometry.
You can look at the DIY part of -http://home.clear.net.nz/pages/grantglazer/Kayak/
This shows the path. We had a manufacturer here who couldn't get the message and blamed the system.
It sounds like who ever designed the Epic pedals missed the point.
And no, wire won't work as the bends are too tight.