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I think I heard about this suggestion some time ago. Can you please be a little more specific so I can locate some illustrations. I've wanted to do a diorama of The Battle of New Orleans. I have ideas for pirates and Indians. Not sure what artillery to use either. I'm pretty sure I read there were Scots light infantry in trousers at the battle,but thought I'd go with Strelets Highlanders advancing like in the movie "The Buccaneer".
Strelets' American Militia in Winter Dress 1812 and Tecumseh 1812 are a shoe-in (http://www.strelets-r.com/Pages/Campaign.aspx?CamID=15)
As Steve has said, Hat Belgian infantry make the best US regulars (http://www.plasticsoldierreview.com/Review.aspx?id=601). You could always use the Netherlands militia (or Peninsular British) for any that you want to do in a stovepipe.
I have used/am using Hat British sailors as the pirates (guns and crew, http://www.plasticsoldierreview.com/Review.aspx?id=644). Also the Imex Alamo Defenders (http://www.plasticsoldierreview.com/Review.aspx?id=183) as figures for Kentucky militia and US infantry in hats.
For the free men of color I mixed in the odd Revell cowboy (http://www.plasticsoldierreview.com/Review.aspx?id=302) as a Choctow Indian, Hat Spanish guerrillas, Imex Alama defenders, Hat French Light infantry (http://www.plasticsoldierreview.com/Review.aspx?id=632).
Major Plauche's militia may have worn uniforms of the French Imperial Guard Grenadiers--*may* is enough for me!
If you have not found it already, check out Chuck Smith's marvellous blog 'War of 1812 Wargaming' http://warof1812wargaming.blogspot.com
To add to Steve's reply (riding the coat-tails again! :) )
The heads/hats from the Imex Alamo regulars with peaks removed and a little dob of putty/modelling clay put onto a British line figure does nicely for these Scots'. Now, of course, there are Strelets' figures that can be decapitated.
I missed the artillery in your previous (save for the naval/pirates). For US regulars I simply used converted Airfix British infantry as I did not have any spare RA gunners. British guns are perfect for the field guns.