Whatever you do, make sure that there is no play or wiggle to the loose band. That can affect vibrational consistency of the barrel and potentially affect accuracy.

But remember, this is not an F-Class rifle. It is 110+ years old and has been shot a lot over the years. If you can approach MOA accuracy, you are doing extremely well.

Shoot it and have fun no matter how well it shoots. It's a Krag!