Re: run dry or not??
I drain mine with the drain screw, running the engine dry is considered a bad idea since one cylinder will run out of gas before the other and be running without oil and you never actually get all the gas out of the carbs but some guys have done it for years with no ill effects and others swear by Stabil.
No longer than the winter can be in NM I would just stabil it and be done, I am in Indiana and my winter last 5+ months.
So really any of the above are fine but if you are going to drain them use the drain plug on the front of the carbs, the "right" answer depends on who you talk to.