You're overthinking this.
The 3CS has three input leads - the big red and black ring connectors that pull power directly from the battery, and a smaller relay lead (with a positap) that taps into any existing switched lead on your bike to tell the two switched plugs on your 3CS whether to be on or off.
- Find a spot to stash your 3CS under the seat. Take the fuses out.
- Take off the bike battery leads and connect the 3CS ring terminals.
- Locate a switched wire in the tail of the bike like the one that powers your license plate light. It will be an orange wire (possibly with green dots on it).
- Tap into it with the positap on the relay wire. See the EB site for directions.
- Your 3CS is now installed (minus fuses).
- Look at your Oxford connectors. There will be red and black power leads with more battery ring connectors. Cut off the ring terminals.
- If you are confident installing one of the connectors provided with the 3CS onto the Oxford red and black wires (following the EB site instructions) do so now. Make sure that when it's plugged into the 3CS the red and black wires match up.
- If you are not comfortable installing terminals, you can cut off one of the 3CS switched sockets and just join those wires with the Oxford power leads with a posi connector, matching red and black again.
- 20A fuse in the 3CS main holder, 10A in the fuse box (in the position where the wire color matches the one you just hooked up to the Oxfords.
- Turn on the bike. The Oxford controller should be powered.
- Install the rest of the grip kit per the instructions.
- You're done. The grips are pulling power right from the battery via the 3CS, no strain on your factory harness.
This is an unswitched 3CS (under the tank support on the left) plus a separate relay (zip tied to the frame at lower right) but the parts are the same.