If you are going to go to the trouble of running new wire I would run a separate wires to each side. 12 ga would be OK.
The reason I would do this it would be easy and the hard work done in case you would decide to use the Tuson sway control device in the future. Right now the device is not available to the general public. But if the device does as advertised and goes on the market it should be on all trailers.
A good controller does not really care if there is some voltage drop. The controller should raise the voltage as necessary as required. This assumes the controller can be set at a gain setting less than maximum.