Have you ever found a solution to your problem? I noticed that my battery is also draining when I completely shut it down. It went from 100% to 95% after about 24 hours of shut down (not hibernate and not sleep). I hope Microsoft acknowledges this problem and finds a solution to this.
Also does anyone know if the battery drains at all after hibernating for a day or more?
After skimming the 11 pages, it sounds like people who put it on hibernate experience 0 battery drain? which almost sounds weird if shutting down the surface completely causes battery drain, but hibernate doesn't.