According to Don Stith and Jerry Gnemi, two of the most knowledgeable Hawken students/collectors the majority of existing Hawkens have tapered barrels with about 10% being straight or swamped. Both men have handled far more originals than any one else still alive.
As I am sure I have posted here before, Hawken barrels are mostly tapers with straights and swamps being the rarities.
Don Stith. Mine is 1.040 taper to .970 and 37" , and 52 cal. Full stocks tend to be smaller barrels with less taper than the half stocks. Personally, I would not go larger than 1 1/16 at breech. With a flint tang I would go 38" long
The very fancy silver mounted 1836 Atcheson/Atchison Hawken on loan to the BBHC for instance has a swamped barrel with the following measurements:
1) 37" long
2) 54 caliber with 7 grooves 1/48" twist
3) 1.125" breech (note this is larger than Don recommended but), midpoint swamp 15/16", muzzle 1"
The Peterson Rifle, which is very similar in stock shape to the Atcheson and shares the same type of shotgun lock does have a slight swamp and may have been cut down (at the breech?) from a longer full-stock (note the extra long fore end and the placement of the wedges - more like a full stock.) This rifles always reminds of this period statement:
Well Don some rifles were re-stocked in the west and can be documented..
"Many years before, a trapper emplyed by the American Fur Company had taken it on a trapping expedition in the Blackfoot country. The Indians killed him and took his gun, Years after, Messrs. Bent, St Vrain, and Company sent an expedetion to that nation on a trapping and trading trip, and traded for the old rifle. At the fort it was re-stocked (full-length), and altered from flint lock to to percussion, and kept at the fort for a target rifle for several years. In 1846 I had it newly grooved (rifled), half stocked, and added a new lock and breech pin (all done by J & S Hawken, of St. Louis, and so marked), and have carried it in all my travels in the trade except on my last trip...(It was) my old and trusty friend, companion, and bedfellow, who never went back on me - "Old Blackfoot" - the name it was known by at the fort and which I have always retained."
Josiah Webb, Adventures in the Santa Fe Trade 1844-47
note: the fort is Bent's Fort in East Central Colorado. Established in the mid-1830's. The fort inlcuded such "conveniences" as a full fledged blacksmith/gun smith shop, a billiards room, and ice house.
The Kennett Hawken from the early 1850's, is also swamped mid-way not towards the muzzle.
Barrel lengths on originals run from short 32-34" on up to 42" on a few early full stocks with a good average being 36-39" long. As for current swamped barrels being incorrect for a Hawken I respectfully disagree - there are just too many variations in the originals to say the new ones would be totally incorrect - while most were less swamped then currently there are some models that come close. Unless that is you are making a bench copy of a particular rifle then yes a custom is the way to go.
IMO - for appropriate modern standard swamps - especially with a bit of adjustment
1) The 42" Rice southern classic - in .50 Caliber
2) The C weight 42" York/Golden Age - in .50 or .54 caliber
3) The C Weight 40 15/16" Reading - in .50 or .54 Caliber
They could all be "adjusted" to a lesser swamp by cutting 2-4" off the muzzle This would make them 38-40" long and would eliminate most of the higher flare, making them closer to the extant originals. But again there were lots of variation in not only the Hawken built barrels but also in other made barrels of the era, including those by Henry and several others that were widely used on western rifles of the era and we know that in some cases the Hawken shop bought pre-made barrels or at least blanks that they then rifled..
The Bridger is as noted, most definitely a swamped barrel not a straight as are the majority of Samuel Hawken stamped rifle (whether they were built by Sam, William, or Gemmer.) I handled it and measured it many moons ago and IIRC it is 1.125 breech and slightly over 1" muzzle 36" long - again IIRC the barrel sold by TOTW for the Bridger Hawken is correct.
GRRW did make some nice rifles, but most/many were not exacting copies - they often used what materials were available such as the coil spring locks used in some models. Again very good rifles (and some of the best barrels I ever used) but basing original Hawkens on the GRRW guns is IMO not a good idea. FWIW - I knew and was friends with several of the crew including Greg Roberts and Phil "Blue Jacket" Sanders - I almost went to work for them in 1974 building barrels, but got a better offer money wise anyway elsewhere.