I'm not sure whether Vermont wouldn't just end up being annexed by the British into Quebec or by New York into NY State. Either way, I don't think it would survive too long.
Why wouldn't it just be it's own small, rural province?
Another idea I like is Vermont as a North American version of Uruguay: a small, homogeneous state sandwiched between two giant federations.
Given the landlocking, perhaps a more relevant comparison would be Mongolia.
(Of course, it's only "small" in geographic area compared to its neighbors...)
Or Paraguay without the Guaranis
The question is what happens to Maine-area and New Hampshire in this scenario. Would they be tempted to join and would they, especially Maine, be allowed to?