So how long does it take to establish residency in most states? @Maj. Bill Martin
Well...that's the question, isn't it? Some states only require only moving to that state, and taking actions/stating intent to establish a domicile.
So I just checked D.C., and it looks like you need proof that you have a residence there -- mortgage or lease, and utility bills. That's for their DMV. The more broad "resident" status for taxing purposes say you must be "domiciled" there. That usually requires taking some steps establishing intent, like filing to be taxed in that location, etc.. But that usually doesn't require a specific amount of time as much as simply the expressed intent to stay. And of course, it wouldn't have to be D.C. He literally could pick any state with the lightest standards.
Once he figured that out, he'd likely do some of the steps before the election, like renting some place and getting bills in his name, etc.. Then if he won, he'd simply have to announce he's moving to that state, go there, and do the final steps. Obviously would have to resign the governorship quickly. But legally, I'm pretty sure it could be done.
Different situation if the residency requirement applied at the time of voting, but it doesn't. Just has to be at the time electors actually vote in December.
