Barrel reboring and relining smiths are picky about what they work on. For liability reasons, they specify minimum barrel diameters and muzzle wall thickness. This especially applies to an antique rifle such as yours, with 30" long barrel and over 130 years old.
Rebarreling is probably a more feasible way to restore your rifle to shooting status. If you care to contact a rebarreling service, try doing a Google search for "la bounty barrel relining".. The outfit that bought Cliff La Bounty's barrel reboriing business continues to operate in Oregon. Cliff was one of the top barrel relining and reboring shops.
HTH
John