It wasn’t a stalemate. The Brits failed to dominate us and control the sealanes. If it was a stalemate we’d all be speaking British driving on the left and drinking warm beer
Sorry, it was a stalemate. We went into the war with conquest of Canada as a, possibly the, primary goal. We obviously failed in that. The war ended with status quo pro ante as the terms, which is pretty much the definition of stalemate.
For what you say to have occurred, it would have required America to lose and be invaded and conquered.