It is not unprescidented that non-resident property owners vote at town meeting.
Connecticut law allows non-resident property owners to vote at town meeting however that right appears not to be extended to city or town elections or ballot questions.
As fair as this system is, it is unique and unlikely to be approved by those in power now or in the future in NH since quite frankly we are their cash cows!
HERE is an interpretation of the Connecticut law that gives non-resident property owners at least SOME voting rights.
However as you can see even in Connecticut where the state law says non-resident property owners can vote it can be a challenge to exercise that right!
Secession is a difficult thing and usually brings more headaches than anticipated. Working toward giving all taxpayers some kind of say in how the money is spent would be an approach that might be easier to sell or at least more difficult to defend against!