The treaty of Ghent never addessed the impressed sailors from American ships, which was reputedly the cause if the war.
From my British viewpoint, most of the sailors were from British ships. American ships paid more, so a number of British sailors absconded, the boardings were to reclaim them.
Also, with Britain at war with Napoleon the military forces were fully committed.
The only forces were a few regular regiments and trained militia, as well as most of the native Americans under Tecumsa, the only obstacles were the terrain. So a possibility of a land grab was in the offing. Though many American States were neutral, prefering to trade than destructive war. When the Peninsular War was over, the entire well trained and experienced British Army and Navy turned to Canada. The war would probably have been won by Britain with these new forces.
This is not meant as a detailed analysis, just a few points not covered in your paper.