Slavery might be a wedge issue in this scenario. Also, some states might reject the new Constitution, since the purpose of the convention was to reform the Articles, not draft an entirely new document.
If you want to keep it reasonably close to OTL, if I remember right Rhode Island almost rejected the Constitution but ultimately decided it was in their best economic interest to accept it. Most of the U.S. going per OTL but Rhode Island becoming this independent little trading/whaling depot might be interesting.
(Or "a wretched hive of scum and villainy" full of pirates and the like. After all, it was nicknamed "Rogues' Island" at one point. Perhaps after a few years of independence, it becomes such a problem for the rest of the U.S. that they invade and conquer it.)