If any of those states offered a widely-accepted non-resident permit, you'd be in good shape. As it is though, it's a real maze with the states you mention.
Of these states (VT,MA,ME,MD,NY),only Vermont will honor your NH permit. for all of the others, none of them appear to have reciprocity agreements on non-resident permits-- so you would need a separate non-resident permit for each of the other four states.
Maine is a "shall issue" state, so you could probably meet the requirements easily.
As far as Massachusetts, New York and Maryland are concerned, all I can say is "good luck". These are all "may issue" states, which means they can deny your application for whatever reason they choose unless you can meet the strict restriction requirements and be able to demonstrate your "need" for the permit. Like I said, good luck-- particularly in New York and Maryland, both of which are increasingly anti-2A.