You probably want to solve the 'chamber question' before putting too many resources into this 1903 barrel.

FWIW - I use to have a Krag that was sportered by Sedgley. Its barrel was a 1905 Springfield Armory barrel, that was originally chambered in .30-03.

Sedgley shortened the barrel slightly at the breech end, re-chambered it for .30-40, and crudely 'notched' the breech for the extractor claw. The date, S.A., and 'Ordnance Bomb' ended up on the bottom, instead of on top of the barrel.
The chamber on this 'reused' barrel accepted factory ammo without problem. It was gentle on Brass and was the tightest of my Krag chambers.