'King carp' - Your original Krag Sling was mainly a 'carry-strap' and not really a shooting aid.

The later 1907 Sling 'psteinmayer' suggests was designed to be an aid in the prone and sitting positions.

It would be interesting to see a close-up picture of your front sight protector. It may be an O'Hare or other 'custom' protector/muzzle cover that was favored by target shooters. These devices are rare and expensive.

BTW - The letters in your 1898-dated stock 'cartouche' are J.S.A., for Joseph Sumner Adams, Asst. Foreman - Assembly Room, Springfield Armory.