Michigan Flinter - go South, young man.
I have one Stephen P. Pool Kentucky, converted from flint, actually made in Kentucky. Mr Pool was from North Carolina, moved to Kentucky. Barrel 46-1/4" swamped .45 calibre, larger at the muzzle than at the breech.
I'da swore I had a series of measurement but did not keep them. As someone above said, contact Jerry Nobel. My rifle is shown on pp192 - 193 of Shelby Gallien's book Kentucky Gunmakers, Volume I.
I also have an iron mounted rifle I believe to be Virginian, also converted from flint. 43-3/8" long .42 cal barrel, rifled 7 grooves. Muzzle 0.938", narrows to 0.832 about 8" back from muzzle, then to 0.862 at breech.
Both of my rifles are in original percussion converted condition. I like old stuff. Welding the barrel & nailing on some pieces of modern cast iron does not appeal to me.
With enough ambition I could get to it & measure Pettypool in some detail. Once after a nice man is finished sanding & varnishing our floors. Fun.
Anyway, that was the style, I believe, in areas of the Southeast.
From what I have seen, contemporary swamped barrels appear to have much more extreme swamp than the majority of original American late 18th - early 19th century rifles. Guess they sell better. Or meby its just my old eyes.