Welcome!

From your description, it sounds perfectly correct. Model 1899 Carbines are the type most often encountered, and, unlike earlier versions, are very seldom faked.

Yours would have been too late for the Spanish-American war, but could have seen service in the Philippines.

You are welcome. Krags are fun shooters and make excellent hunting rifles.

I did not check your serial number, since the process is so often fruitless, but will do so tonight if someone else with the SRS books doesn't come along first. Records have survived for about 5% of the numbers. If your number is listed, I will provide the address for requesting a letter. IIRC, they cost around $100 now, and often have a couple of months waiting time.

Pete:  Welcome to the KCA Forum.
  If your Krag, #354893, is marked Model 1899 on the receiver, it was built as a Carbine.
  Krag receivers were marked and numbered, before assembly, and then went into parts bins.  U.S. Krags were not assembled, inspected, or issued in numerical order.

Your Krag was assembled around November, 1901.  The closest serial numbers of "known Krags", listed in Frank Mallory's, "The Krag Rifle Story", second edition, are model 1899 carbines.  (#354871 - 1899 carbine, documented 2/19/1936, 2nd corps area & #355368 - 1899 carbine, in RIA Museum).  The listed serial numbers are Krags that were noted in found government documents (As Dick Hosmer noted, a small minority of legitimate Krags).

  The script initials in the stamped 'box' are "J.S.A." (James Sumner Adams), Springfield Armory Sub-inspector.  This 'cartouche' stamp was put on Krags, when a completed arm was inspected and accepted for service.
  Since your Stock is dated '1900', it is likely parts were switched and this Stock was not originally on your barreled/receiver.  This is common.  Your carbine may have undergone Arsenal repairs, updates or reconditioning.  The 'circled P' stamp was put on a Stock when a Krag was tested at the Armory for functioning.  (Some stocks will have more than one "P").
  I am curious which rear sight is on your carbine.  (There are three likely possibilities).  If you post some pictures, you will get a better assessment.

Another shot