Code V626 (NEC to RI) also works for those traveling FROM the RI stations (Providence, Kingston, Westerly) to other locations in the NEC (such as NYP, BOS, etc...). At least it worked for me leaving from my home station (KIN). I just input V626 online, and it took with no problem. So you don't actually have to stay 1 night in the Ocean State.
I assume this discount code is still good, as the fare states "... all unreserved trains ... ", since ALL trains on the NEC are reserved. There are no more unreserved trains.