Then that leaves only two war goals that were actually articulated prior to the war - an end to impressment (which didn't happen as a result of the war) and 'free trade' (which also didn't happen as a result of the war. By that metric the war was an absolute and total failure...
Of course war goals are rarely clearly expressed, particularly in a democracy, and in many (most) wars are so vague, even in the minds of the main belligerents, that actually working out what a 'win' is or how you can win is nearly impossible. So we look at what evidence we have from the statements recorded, public and private, and try to work out what people hoped to obtain from the war. If you do this it becomes very clear that those people who agitated most strongly and publicly for the war had some quite specific war goals that definitely included annexation as an objective.
No doubt, however I think you misunderstand the musings of a few on how the war might be won, and confuse that with occupation of the location will mean that it stays with respect to the peace treaty.
War goals:
1) Firmly establish independence from Great Britain - with respect to citizens rights and trade.
2) Open the right to trade with Continental Europe as a neutral
3) End to impressment and kidnapping of sailors from US ships - British ships would enter US territorial waters for the express purpose of impressing crew.
4) End the trade in weapons to the Indian tribes resisting American expansion in the midwest.
5)
Disputed: Annex Canada (as a means to end Indian raids in the west and foster American expansionism) - since debunked in 2015 by Richard Maass.
The expanionist theme is a myth that goes against the...
Richard Maass said:
relative consensus among experts that the primary US objective was the repeal of British maritime restrictions. (The US went to war) because six years of economic sanctions had failed to bring Britain to the negotiating table, and threatening the Royal Navy's Canadian supply base was their last hope. Leaders feared the domestic political consequences of (acquiring Canada). Notably, what limited expansionism there was focused on sparsely populated western lands rather than the more populous eastern settlements (of Canada).
Horsman points out that the desire for Canada did not cause the War of 1812. I.E.
Horsman said:
The United States did not declare war because it wanted to obtain Canada, but the acquisition of Canada was viewed as a major collateral benefit of the conflict.
Opposition to annexation came from the south (which feared more free states) and from protestants, who feared giving French speaking catholics repbulican citizenship.