Frank Mallory's book, "The Krag Rifle Story", 2nd edition, has references on page 87 and page 97 to Italian walnut stocks.

Mallory reports, on page 87, the firm of Louis Windmuller and Roelker, of New York City, furnished Italian walnut wood for stocks and hand-guards. (13,000 stocks in June, 1899, and an additional contract for 20,000 stocks in July, 1899).

FWIW - I am sure the New York company supplied wood "blanks" and the actual shaping, finishing, and manufacture of the stocks and hand-guards was done at Springfield Armory.

On page 97, Mallory writes about the issue of Krag rifles to the Navy and Marine Corps, starting in November, 1899.

He reports:
...."The first 1,00 (sic) rifles issued to the Navy had stocks of light wood. These were in the 223000 serial number range"....

Mallory goes on to describe 'rear-sight updates' and believed there was an apparent effort to match Italian walnut hand-guards to stocks, during sight & hand-guard updates.

BTW - 'Lead Snowstorms' Krag rifle, #223502, is apparently in this 'Navy # range'. (His rifle was likely produced around August, 1899).

Mallory also reports a couple of "light stock" rifles, #331652 & #332195 being issued to engineers in 1902, to replace "dark stock" Model 1898 rifles.

The Italian stocks, that I have observed, generally have 1899, 1900, or 1901 dates in the J.S.A. acceptance stamp ("cartouche").

'Musketjon' - You said your Krag was built in October, 1898. I assume, it is in the 133K to 142K range?
You did mention it had gone through an armory/arsenal "rebuild", at least one time.
It is quite likely, when disassembled for 'refurbishment', parts got switched and the current stock is not your rifle's original stock. (Not that it should matter).