If you decide to try to unscrew the breechplug, let some good penetrating oil like Kroil soak in for a bit. You can grab the barrel flats in a strong vise with padded jaws. I use leather. A pair of fitted hardwood bocks can be made as well. They can be finely fitted to the barrel with bedding compound. You will need a wrench that fits the breechplug properly. With your barrel, I would apply the receiver wrench that I use on flat sided receivers to the top and bottom flats of the patent breech plug. If you apply pressure and either the barrel shifts in the vise, or the breechplug slips in the wrench, damage will occur. With the breechplug out, cleaning and inspecting the bore is much easier.
I would agree with the suggestion that lighter loads would be appropriate - that barrel doesn't have the dimensions of a Hawken.
I just pulled the nipple and breechplug from a W. Richards, 13 John St. London stalking rifle. Both came out cleanly, after wiping the bore is shiney with some minor patches of pitting. It is a bit heavier than you barrel.
Those are post 1813 Birmingham proofs, so the rifle likely predates 1855 when different marks were introduced.
Have been restoring a halfstocked hunting/target rifle by GH Remington, Rome, NY. Drum and breechplug removed easily enough. The bore was plugged for four inches at the breech with rust and crap. Had to use a drill bit on a rod before I could see light. Have been using "Evaporust" from Lee Valley to soak the bore. This stuff doesn't instantly attack rust, browning, etc. But it has really helped with the bore. I fill the bore, leave it for hours, drain, pull the plug, brush well, repeat. Bore isn't going to be great, but it might lap out well enough to shoot.
