Meplat, your barrel is a 1x36" Green Mountain .54, right? Do you really want a 37" barrel (with the patent breech)? I've cut some of mine to 32", which makes for a handier rifle. There are originals that have 30.5, 31.25, 32.5, 33, and 34 inch barrels, plus likely 36" also. (I calculated these lengths from photos in John Baird's book "Hawken Rifle, the Mountain Man's Choice"). So you can cut it off if you want to. The stock forend does not get changed, (the 30.5" barrel is a heavy one with a shorter forend and a shorter length of pull. It also has a checkered semi-pistol grip and a big tang mounted peep sight (See also R.L. Wilson's book "Steel Canvas", page 85). You have to cut off the underrib anyway. I scribe a line around the barrel with a square and hacksaw it with a 32 tpi blade. File mooth with a flat file. Check for square. Debur. Took me 20 minutes yesterday. I am also going to cut off my 36" .54 Green River barrel, which I am building into a second Kit Carson rifle, and yes I know about GRRW's "choke".
Two friends who built barrels for the old GRRW told me not to worry about it. I have the catalog from GRRW from 1978 when I built a Leman in their shop, and it says "P.S.-Please don't cut the muzzle off our barrels if you want to shorten it. If you do, you will cut off the choke and lose accuracy thereby. Always shorten the barrel from the breech. May you be forever haunted by the devilish spirit of lost accuracy if you shorten from the muzzle!" (Neill Fields told me the "choke" was a function of how the barrel was rifled, and not something deliberately done. He has no misgivings about cutting it off. And Carney Pace, who worked there, doesn't either. He said I could lap it back in if I wanted it, which I don't. Other modern barrel makers do not mention choke, so it isn't even there in your Green Mountain barrel.