It seems that everybody is settling for too late a BP.
It is entirely possible for a massive British victory in the war without substantial investment on their part.
BP #1:
Issac Brock does NOT die at Queenstown Heights, but after capturing Scott's advance force as in OTL, holds on to and secures Forts Erie and George.
Then he moves west, and after the triple capture of Michilimakinac, Dearborn, and Detroit, pushes on towards the River Raisin, assuming a defensive position when Harrison arrives. At this point, with Brock instead of Proctor, it is possible for the British to capture Fort Meigs or Stevenson, and even if Perry wins on the lake the British at minimum still hold Michigan territory.
#2:
ANYONE BUT YEO is in command of the British forces on Lake Ontario. Both he and Chauncey on the American side refused to attack each other. Both forces saved their best for Lake Ontario, and Yeo had a slight advantage. If there was a major naval battle, probably the British would win. This would lead at least to the loss of Sackett's Harbor and probably inroads along the Niagra.
#3:
Top 2 officers of the Queen Charlotte are not BOTH wounded minutes into the Naval Battle of Put-in Bay. Even though Perry had the stronger force, it is generally agreed that he won when the Niagra was able to pummel both of the strongest two British ships simultaneously, and this was only because while turning, the inexperienced lieutenant on the Queen Charlotte rammed her into Detroit. If they remain maneuverable, then the Niagra can be destroyed by superior firepower, at which point the British would have destroyed both of Perry's capital ships, and he would lose.
This would prevent Harrison's invasion, and again lead at minimum to holding onto Michigan Territory.
#4:
ANYONE BUT PREVOST is in command of the drive down Lake Champlain. This one is self-explanatory.
#5:
British are actually smart at New Orleans, and follow the battle close to as in 1812....I forget the title, but it's a great AH book.
#6:
Just about any BP in Europe enabling Napoleon to be "defeated" by or before 1812. There are probably millions of ways to do this.
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The Americans were very lucky to secure Status Ante Bellum in the end, this due primarily to Harrison, Scott, Perry to a small extent, Macdonough to a GREAT extent, and the natural geography of Baltimore.