I went to Cody and measured the Liver Eating Johnson Hawken. The barrel is 31.75" long ahead of the snail. It is 1.3" across the flats ahead of the snail and 1.218" at the muzzle. The bore has 7 lands and grooves and the twist is 1 inch in 48 inches. The bore I measured with bore gauges I make as .537 (call it .54 caliber) and the muzzle is filed, at least .58 across. The museum uses as tapered brass bore gauge, so they don't read the bore diameter. You can get a custom barrel built to these specs by Oregon Gun Works or Bobby Hoyt, but you couldn't get a breech plug and tang to match. Better to get it 1.250 at the breech and then use Track's Hawken Plug-PH-20-3, 1 1/4" slant with 3/4x16 threaded journal 1/2" long. If you want a lighter rifle, go with a 1 1/8" straight barrel. Underrib is 18.125" long, riveted on with 4 rivets
Mountain Meek gave you the correct part numbers for lock, butt plate, triggers and trigger guard. Toeplate is a beavertail. No commercially available correct entry pipe, I'd file one out of the TE-7-I, 2.6" long, opened to .480 inside diameter. Rod pipes are .500 inside diameter, 1.26" long. Ramrod had a concealed ball puller on the inside end, .400 at wood, but .500 at the muzzle end. Lock was 4.9" long, hammer was notched. Lock panels are 1.710 across the front and 1.5 at the rear.
Stock is 2.1" deep ahead of the trigger guard and at the keys. No fish belly to toeline or forend. Rear sight is thick, closest I could come is Track's RS-PA-11, cut to a 3/8" base. Best stock is Pecatonica's halfstock Hawken for a 1 1/8" barrel (you'd have to inlet the 1 1/4" barrel in, no problem), drilled for 7/16" ramrod (1/2" to entry pipe, then can reduce to 7/16" diameter with a rod tip inside). No inletting other than barrel and rod hole. Drop at heel is 3", which this stock has. No cast off, and pitch (butt plate flat on floor and tang touching a vertical wall) is 5 inches to top of barrel. Nose cap is .75 long, cast steel, Muzzleloader Builder's Supply lists the correct one, but is out of stock. Otherwise go with their 1" size (.8" long) and file open to fit the barrel. I get a Davis Jim Bridger lock not cut for snail and cut my own so the hammer hits the nipple correctly.
I also did the pistol grip Hawken, the W. S. (Denver) Hawken, and 1997.4.8 (with a patch box). I was too beat after a bad night's sleep at the IRMA (Buffalo Bill's) hotel with hammering steam radiators to do any more. I have a few pictures and will be getting high quality photos from the museum in a few days.