The biggest consideration is whether or not you want to keep paying NY state income tax. Most people leaving the country would want to establish residency in a state without income tax, to remove that cost and hassle. But to do so, you would not only need to remove your NY residency, but establish in the new state. (i.e. drivers license, register to vote, etc.) The only issue I would see in having the two addresses is the two states you have chosen are both "sticky" in terms of income tax. You might be contested for both. I would not hand in your NY drivers license unless you were going to get one in another state. You do have to consider the logistics of renewing it, when the time comes--either time your visit to renewal time, or plan far ahead--likely, farther ahead than their normal process allows.
You say you will be out of country for 11 months of the year. Where will you be in the US? Will you always go to New York? Do you have family there? Or will it be to visit a variety of places? If it was always NY, you might get into contention about residency, if you established it elsewhere.
I don't think Vanguard or Fidelity will care. That's why they have multiple addresses in their database. Every snowbird ever will have at least 2 addresses, in different states. It's not uncommon.