Earlier models continued to use the M1887 trapdoor sling. It wasn't great because it has to be completely disassembled to be re-configured.
In the South Pacific the Mills web sling was used as the M1887 was prone to rotting and disintegrating in the tropical environment. The Mills is somewhat similar to the Enfield sling you have now.
The Kerr NoBuckl which came later was used throughout WWI and either could have been on a Krag in the rear or back in the states.
Around the turn of he century there was a series of short lived models of leather slings that eventually became the M1907. The major differences were in the number size and shape of the hooks and buckles. The exact model for my Krag would have been the M1903 which isn't reproduced so I'm using a M1907 instead.
If you can't tell I did extensive research on this subject after I bought my Krag.
For shooting utility - go with the model 1907 sling.
The 1887 sling was primarily a carry strap.
It is very clumsy because it's too long & bulky for the Krag.
(The 1903 Army NM Team made a creative use of sling and swivels).
The Mills Krag canvas 'Tropical' sling was a failure.
The Brass 'C' Hooks were too narrow and caused the strap to curl.
The Lee-Enfield (Mills) sling works well, but it is not correct.
As I had stated earlier the Kerr would be correct for the WWI era which is when it was first adopted. If you're looking to make it turn of the century correct you're going to have to choose between a M1907 or M1887. I have a repop Kerr on my US Model 1917 and it's excellent. Truly a marksmans sling and very easy to reconfigure. No wonder the Marines adopted it in 1917.
These are on the bottom of the wrist just behind the trigger guard. I'm guessing the "Circle P" is the proof mark? What about, what appears to be, the number 80 above it? Just another proof/inspection mark?
The circle P is the firing proof mark. The 80 could be anything from a proof mark to a rack number. My Krag rifle has a tiny S where your 80 is, meaning unknown.