Your metal does not look that bad to me. There appears to be lots of finish still on your barrel.
Using small #0000 steel wool pads soaked with penetrating oil or Hoppe's #9 will remove light surface rust and not harm metal finish and patina. Use just a light pressure and keep things moist with penetrating oil.
Heavier scale can be broken down with a worn bronze bore-brush, copper penny, edge of a discarded brass cartridge case and penetrating oil.
I have had luck with a mixture of linseed oil & pumice or rotten-stone, used with the edge of a Popsicle Stick, to create a 'slurry' and burnish a rusty barrel surface into a pleasant patina. Go slow and occasionally wipe off mess with paper towel to check progress. (Repeat process until happy with results).
Aaron, I don't know if you are familiar with original Krag finishes. The various metal parts received specific and different metal finishes.
The metal was not a uniform "Bluing".
Krag barrels were rust blued (officially called 'browning').
The Reciever, side-plate & magazine-door were case-hardened. This was mottled colors that often turn silvery with age.
The Bolt body was polished bright. The extractor-spring was flame blue. The striker-knob and bolt-sleeve were case-colored. Screws were blackened.
BTW - Original Krag American walnut stocks were stained at Springfield Armory with Logwood, which gave a reddish-brown color, prior to getting their linseed oil finish.
An original Krag rear sight will hide the unofficial 'dovetail' that was added to your barrel. The Krag sight screws are a peculiar 30 tpi. Reproduction screws are available from S&S Firearms, Glendale, N.Y.
(FWIW - I have Krag #81028. It is a cut-down model 1896 rifle. I recently fitted it to a poorly cut-down model 1898 stock, to make what I call, a 'Faux' or false 1896 Carbine. The front-sight is a 1903 Springfield sight, so no one should be deceived in the future).
