New Orleans wasnt too important beyond the PR front (battles tend to have lacklustre effects when the war they are fought for is over). The biggest effect its gonna have is on the native population east of the Mississippi and on the Bank of The United States.
Do you think there might be no trail of tears with say Clay or Adams in the presidency?
I wonder what effect the 'Five Civilized Tribes' will have on the US given a president that might be more inclined to agree with the Supreme Court.