The Stevens-Pope barrels were made 1901-1904 by Stevens.  They were intended to turn any US military Krag into a trainer with a minimum of parts.  They were sold on the civilian market and were also purchased by at least 4 different National Guard organizations. 

As you describe, the barrels were bored off center, with the muzzle concentric but the chamber at the 12:00 position.  That was so that the military Krag bolt could be used with no modifications.  The firing pin strikes at 6:00 and the regular Krag extractor extracts the case most of the time, but not always.  If you shoot the rifle (you should), take along a good .22 caliber cleaning rod.  If a case fails to extract, use the rod to push it out.

Also, there is a tendency for fired cases to get stuck between the bolt and the side plate.  Many users removed the side plate to solve that problem.  Sometimes the side plates get lost.

I have been trying to learn about the Stevens-Pope Krag .22 rimfire barrels for years.  Yours brings the number traced to either 8 or 9.  I may have counted one twice.  In my book, that makes your barrel pretty darn rare.

I have no idea how many were made, but Springfield made more than 800 GPRs to replace them.  Note that the Model 1898 Gallery Practice Rifles have a different chamber & extractor system, a hole drilled in the left side of the receiver and are marked ".22 cal" on the left side.