Dutch, you are correct to say Hawken barrels with SLIGHT tapering. I have measured some originals. Here are the results: Jim Bridger Hawken, barrel 33 1/4" long ahead of snail. Measured 1.175 ahead of snail and 1.125 at the muzzle. That is the thickness of a dime, half of that taper per side. Green River Rifle Works had that rifle from November 1975 for about three years. I handled it there in 1978, we took the lock out in a class I took there. Carl Walker, their gunsmith, said the barrel was not tapered, "you can make that much difference with a file". My avatar at left is me holding the Jim Bridger Hawken in the museum in Helena. MT.
Kit Carson Hawken: barrel is 31 1/16" long ahead of snail and 1.125 ACF (across the flats) there and 1.022 at the muzzle, according to others who have described it. I have not personally measured this one. That difference is .103, or about a dime's thickness taper per side.
I measured a S. Hawken rifle in a museum in Cheyenne, WY but can't find my measurements. The barrel was 35 1/2" long ahead of the snail (AOTS). I don't remember a taper. Then I went to Lincoln, NE and measured the S. Hawken rifle in the state museum there that Robidoux made mechanical drawings of. That barrel was 32 1/8" long AOTS and measured 1.125 there and 1.090 at the muzzle. That .035 is half a nickle thickness total, or 1/4 (.0175) a nickle thickness taper per side.
Last December I went to the Cody Firearms Museum and measured some originals. Liver Eating Johnson's Hawken barrel was 31 3/4" AOTS, 1.300" ATF there and 1.218 at the muzzle, or about a dime's thickness taper per side.
The Pistol Grip Hawken there had a barrel 32 9/16" ahead of the snail, 1.145" ATF there and 1.155 ATF at the muzzle, yes, slightly larger. Only a matter of filing. I have an Oregon Rifle Barrel Company .54 barrel with a 1-48" twist (1 1/8" like the original, recently made for me) I am building into a copy of the Bridger Hawken, and that barrel varies from 1.120 to 1.140 midway to 1.130 at the muzzle. Just a matter of filing it true, if one wants to take the time).
The S. Hawken with a patchbox at Cody has a barrel 31 13/16 AOTS, 1.00" there and 1.00 at the muzzle.
The W.S. Hawken (Denver CT, with the C stamped backwards) had a barrel 32 1/4" long AOTS, 1.130 there and 1.010 at the muzzle. That is about a quarter dollar's thickness per side.