The best the Americans could probable do is with a POD in 1807. After the Chesapeake Affair Jefferson takes a different tack. No embargo, that was just stupid, but raise tariffs. The embargo destroyed the influence of the Republicans in New England. The tariffs would help accelerate the development of industry, at least in the North. Use some of the money to build more warships. New England would like the money from ship construction. Build a fleet with 4 Razee's, these are Ships of the line cut down a deck, a razee can take on a small ship of the line, like a 64 gunner. 4 more 44 gun frigates, and 4 more subscription frigates, that means ships paid for by money raised by citizens in States, plus other smaller ships.
A fleet of that size and power could take on the ships of the OTL RN squadron on the North American Station. The RN was shocked by the 44's, they probable underestimate the razee, and think a 64 like HMS Elephant with the 4 frigates with her would easily defeat what look like 5 Yankee frigates, they could take in one battle. All they'd see was easy prize money. The shock of losing a whole squadron, including a capital ship would hit like a tidal wave in the Admiralty.
Raise the size of the army to 10,000 men, and improve training of State militias, New England had the best funded, and trained. The Federal Government should help fund State militias, and provide West Point trained officers to advise on training. Expand the number of openings at West Point to meet the demand for trained officers. Find a compromise with Agricultural interests to renew the Charter of the Bank of the United States, in 1811.
With the countries finances in better shape, a stronger army & navy, and less hostility between the Federal Government, and the New England States the country would be on a stronger footing in 1812. Without an incompetent like William Hull Detroit probable never falls, avoiding the disaster on that front at the opening of the war. Launch a coordinated offensive from Detroit, and Buffalo to capture the territory they captured after the Battle of the Thames in 1813. Then launch an early attack on Kingston Ontario, to eliminate the naval threat on Lake Ontario. If they can use New England, and it's militia try to cut the St Lawrence River line.
At that point accept the initial British offer of canceling the Orders in Council. Then offer to withdrew from Canada, in exchange for cutting off aid to hostile Native American Tribes in the United States. The annexation of Canada should never have been an American war objective. Canada from an American point of view is worth more as a hostage to British good conduct, then it would be as new States. Try to bring the war to an end in 1813, the point would be made that the United States wasn't a country to be treated with utter contempt.