Approaching this from another angle since the information isn't yet available:
Have you tried to
really clean this 'coal chute' barrel?
'Shot out' is usually reserved for barrels which have been examined in a clean condition where the ravages of time and shooting have had the ill-effect of degrading the lands. Prior to a few years ago most shooters lacked the ability of being able to actually see inside the barrel to make this determination. Now though, with the advent of inexpensive borescopes, everyone can enjoy the heartbreak of being able to observe ill treated bores.
The 'raised rib and lots of engraving' makes finding a replacement nearly impossible. This is why I suggest trying a thorough cleaning first before giving into the need to make drastic changes. But, if your barrel is truly shot out, then I suggest finding a very careful reboring expert to handle this job. Make a phone call to discuss the process and the details of what you will be sending and what your expectations are. Get their ideas about a cartridge which is suitable. Be thorough in your discussion so you are properly prepared to make this decision as there is no going back.
I suggest these avenues since I was in your position a number of years ago. Mauser M98 with a ribbed barrel and engraved. I scrubbed the absolute bejesus out of that barrel until low and behold the lands appeared in decent enough shape to postpone the rebore. It still shoots to this day with careful attention to a reasonable cleaning procedure.
Enjoy your project!