You certainly put a lot of thought into this puzzler. Yes, the salesman must either start or finish in Maine if he is to visit each state once and only once. And New York state is unique in that it forms a barrier between the New England states and the remaining states — once past NY, going in either direction, the salesman can never return to the section he just left, be it New England or the lower states.
Technically, New York isn’t unique because the same is true of New Hampshire: it’s just that as a barrier it separates the single state of Maine from the entire rest of the country.
And yes, I’ve put a lot of thought into it, but years before it became a puzzler. I wanted to work out an actual route and see if it was feasible. It got a little hinky when one of the routes wanted me to go directly from Oklahoma into New Mexico; there’s a short section of border there but not a lot of major roads cross it, so while it’s actually doable it’s not in any sense practical.
And then there’s the “New Madrid Bend”, where the states of Kentucky, Tennessee and Missouri meet, not at a single point but at three different points a few miles apart.