Cut a length of Cat5 cable (I used 2 feet), and cut away an inch of the insulation on each end. Cut off all but three wires from the exposed areas.
The 3 wires in the cable each will connect to a pin on the remote plug.
Attaching the connector varies depending on what kind of connector, so I will refer to each wire as its pin on the connector.
Connector pin 1(Receive) --- NES pin 3 (this is connected to the PIC's transmit)
Connector pin 3(Ground) --- brown
Connector pin 4(3.3V) --- V+
Once these three wires have been connected, simply push the cable into the stress relief posts that the old cable went through in the controller case.
There is a severe lack of places to tie into the V+ line. All pins that need to have V+ can be connected directly to each other, but NES pin 16 must be at 3.3V. I used a knife to scrape some of the soldermask off of the trace to create my own pads.