Your stock is 15/16 so if you want a 54 cal. look for investarm/or investarm made barrels: lyman trade/plains, cabela's , investarm, some charles dalys......twist will be 1-48 (on all I've seen)
There are also some 58 cal ( 1-48) and 62 cal used investarm made barrels, if bigger is better. I've only seen the 62 cal in smoothie as a lyman plains rifle, I have one.
GM made a 54 "drop in" in 15/16. Might still be available? I think, two twists, 1-28 and 1-70.
I'm pretty certain of the above, but chime in if you can correct me.
I have TCs, charles dalys, lymans, GM and most of these barrels will fit each other with little tweaking (e.g. all the 15/16 "kissing cousins"). I have noticed some tangs place the barrel a slight bit lower or higher, ribs too long as mentioned above, slight need to file a tang/hook, and to tweak the way the staple fits the stock and/or wedge key.
Most all of these barrels will either drop in, or can be made to fit all the investarms made guns and the 15/16 TC hawken.
Toledo Arms also made a 15/16 12ga drop in for the TC, that is just as close in fit as the rest. Unlike the lyman barrel I have the Toledo is choked.
Also some investarm barrels will be chrome bored.
P.S. Lyman great plains is a different animal (stock/hardware/2 wedge keys) made by investarm.