It seems like there is still a lot more to be analyzed on this topic. In OTL in at the end of the war there were already two squadrons of warships each containing multiple frigates and 1 (112 gun) battleship already commissioned and sailing Lake Ontario. If the war had continued, within a year both sides would have had fleets led by multiple battleships and frigates, all contained on a small fresh-water lake. Anyone want to weigh in on how this may have turned out if the war had lasted an extra year?
You'd need a different war. If the British win at Plattsburgh (easy enough to do, regardless of what others say) they might try and push for a longer war.
After the raid on Sacketts Harbor Chauncey was extremely reluctant to leave his main base of operations. And the British building programme in 1815 was equally as extensive as the Americans except they already have a battleship constructed. I don't think Chauncey would sail out and engage Yeo unless something forced his hand. OR... if the St. Lawrence explodes when she's struck by lightning and the battleship race is reset.
Controlling the water the British are probably better supplied in Niagara throughout 1815, there could be more fighting around Buffalo. The British might try and attack Sacketts Harbor by land.
THAT would be a neat scenario for the new year. The Americans have suffered a devastating blow at Plattsburgh in September (but Prevost doesn't really follow it up being as cautious as he is and he's only managed to march south to Saratoga). And Chauncey gets a bit of deus ex machina when the St. Lawrence gets struck by lightning and sinks with all hands, and now control of Lake Ontario is in flux once again. Setbacks and gains for the new year.