I've been meaning to post this mod since last year when I did it but never got around to it. Anyhoo, I basically followed these instructions to have my new thermostat control the AC without running any wires to the AC.
You run a t-stat wire from the t-stat to the power inverter, and a relay cuts power in and out to the AC unit. I've been using it for a year now and it works great. Much better than trying control it with knobs on the ceiling!
In my case the wire just had to run down the wall into the base cabinet below where the inverter is.