The reference books (reference to Brophy) tell us that the twist was 1:28.  Ballistically, that twist simply does not work. 

In Pope's Barrels, Ray Smith has a photo & description of an unfired barrel #836, 30" long, chambered for .22 Short and fitted to an 1896 carbine.  That barrel would have a 1:25" twist.  For 3 years, I used a Stevens-Pope 44 1/2 offhand rifle in .22 Short.  It had gain twist and the fastest (at the muzzle) was 1:24".  I have another Pope barrel in .22 Short (dated May, 1910) on a Winchester 52.  It has a 1:25" twist. 

A 28" twist would be pretty marginal for a 29-grain bullet.  And would not stabilize a 40-grain Long Rifle bullet, not even on a 25-yard indoor range.

My guess (never having slugged or measured one) is that a SP .22 cal Krag barrel would have 8 lands & grooves and a 1:16" twist.  That twist was standardized for the .22 Long Rifle cartridge back in the late 1880s.

Much is written about Peters "Stevens-Pope" Armory cartridges.  They were just ordinary .22 Long Rifle cartridges, 40 grain bullets, loaded with a case full of King's Semi-smokeless powder, giving BP velocities. The difference was that the bullet in the Armory load was crimped into the case. 

Back then, ordinary (and even match grade) Long Rifle ammunition was not crimped.  The bullet simply sat in the case.  All the rifles that used Long Rifle target cartridges were single shots, so uncrimped ammo was not a big deal.  Plus there was considerable argument among serious target shooters that crimping destroyed accuracy.

But the National Guard officers (guys like Charles Winder) recognized that uncrimped ammo was a problem with a military training rifle.  If you had to remove an unfired cartridge from the chamber of your SP Krag, the bullet was likely to stay in the chamber and the powder would spill all over the inside of your Krag's action.  So Peters "SP Armory" cartridges were crimped. 

With revolvers & repeaters like the Marlin, all .22s were crimped.