R.Marshall,
Now I'm back to my original assessment that it is chambered for 6.5x57. This is based on the photo, showing fired and unfired 6.5x57 and 6.5x55 cartridges. We still have the problem of the failure to fire. Except for the spring, the parts in the bolt are 120 year old original parts. Parts don't grow over time, and the rifle wouldn't have lasted through mounting and sighting in of two scopes and 120 years of use if it didn't reliably fire. From the photos, I can't see any repairs that may have been botched. This leaves us with very few possibilities for the cause(s) of the problem. If you told us earlier, I don't remember if it cocks on opening or on closing, and does the sear have the same number as the bolt parts? One of the most obvious changes during the transition was the shroud lock that was added but which was not added to your rifle. The reason for the lock was to prevent the shroud from "unscrewing" itself from the bolt during use. If the shroud is one thread short of being "turned up", there would likely be a failure to fire. The bolt body fits into the shroud when assembled, a foreign object inside the shroud could prevent it being "turned up" fully. The firing pin has three lugs, onto which the "nut" or cocking piece turns. You might assemble the bolt with one fewer of these lugs in the cocking piece, and check the firing pin protrusion in that mode. It is hard to troubleshoot a problem without the rifle "in hand", it is easy to miss something that would be obvious if you can handle the rifle.
Mike