Jim,
Did you get your info from Flayderman's Guide to Antique American firearms? If not, it is reasonably priced and still available. It has around three pages on Ballard rifles and carbines.
It's complicated with many barrel lengths, calibres, octagonal barrels (these not confined to sport), round barrels and part round part octagonal.
It lists the government contracts - Kentucky, New York not marked as such but US government contracts carry MM inspector marks.
I can't immediately identify your model but can read it a bit more closely if you like.
CC
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