It's not really true that you'd have to do an overnight layover if you wanted to get from Maine to Vermont.
Weekdays you could depart Portland (POR) at 5:20am, and arrive at North Station (BON) at 7:50am. You'd have to self-transfer from BON to South Station (BOS) or Back Bay (BBY) to get down to New Haven (NHV) to catch the Vermonter. Following are your connection options, I will leave the connections Amtrak.com offers from POR to NHV, so these will have to transfer between BON and BBY, though you could always go to BOS if you'd prefer.
Depart BBY at 9:20am on Acela 2159, and arrive in NHV at 11:11am. Or depart BBY at 9:36am on Regional 93, and arrive in NHV at 12:04pm.
The Vermonter departs NHV going northbound at 1:25pm. The Acela should certainly be enough time to make the connection, as well as 93 should be a long enough connection. You'd have to weigh out the cost of the Acela vs Regional ticket, and being more likely to make the connection. But nonetheless, same day connections ARE certainly possible from Portland to stops on the Vermonter. Unfortunately, they are not guaranteed by Amtrak.
Edit: Also, I will add my vote for Mystic. Beautiful city, in the right places. Mystic Village is always a great place to visit too!