AHC: Native American Regiment in a US/North American millitary

Your challenge, should you choose to accept it, is to create a world (pre-1900 of course), in which an entirely Native American regiment/s exists in a US or North American millitary force, similar to the Highlanders or Gurkhas in the British army, or the Cossacks in the Imperial Russian army. Bonus points if your POD doesn't result in a drastically different North America.

Personally, I think that a force of "Praying Indians" during King Phillip's War could be interesting, but for that to happen you'd need to limit the influence of Increase "The only good Indian is a dead Indian" Mather on public discourse in 1640's Massachusetts. Of course, sidelining him (in favor of someone else whose name ai can't remember right now), results in all sorts of butterflies as to the larger politics of early New England, which means of course that I don't get any bonus points. Darn.
 
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