King Carp - I will send you a PM later, but, my Two Cents for now:

Your model 1899 carbine, #362073, was likely assembled around November to December, 1901, according to Bill Mook's calculations and in December, 1901, in Poyer's tables.
An acceptance 'cartouche', dated 1902, seems pretty credible.

According to Mallory, the model 1898 carbine sight, was being put on model 1899 carbines assembled from January to July, 1900. Since it quickly became obsolete, it is unlikely a discontinued model 1898 carbine sight would be found on a carbine made 1 and 1/2 years later.

IMHO - model 1901 and model 1902 carbine sights are both correct on your carbine.
Since your hand-guard and stock match so well, it is possible this carbine once wore a 1902 carbine sight.

A common belief is that around 1903, the model 1902 Krag sight was the preferred service sight.
A variation of it was adopted as the sight for the new Rod-Bayonet 1903 Springfield.

In 1905, major changes were made to the new Springfield Rifle. This included a new rear-sight with features similar to the Krag model 1901 rear-sight.

Likely, the model 1901 sight then became the preferred sight for Krags still in U.S. Army use and the model 1902 sights saw a lot of National Guard use.