K grade is for a 1900 grade.
Serial number is for a 1900. All K grade are in the 300,000 range. All 1894 are in the 100,000 range.
Snap on forend is for 1900.
In your last post do you mean that it is stamped with the 1894 patent? That stamp should say " Patented October 30, 1894" You wouldn't be the first to be confused by that stamp. The 1900 is essentially a simplified 1894, designed to hit a lower price point. Streamlined mechanicals, cheaper wood, no ornamentation at all. Much like a Fox Sterlingworth or Parker Trojan. That is why it carries the 1894 patent stamp. Having said that, they were still nicely made when compared to all other American makers' (the big six) opening price point guns. The only maker that compared to Remington in quality of manufacture was Parker. Fox, LC Smith and Ithaca for example are crudely assembled in comparison. And the Remington is the only true Anson and Deely style boxlock made by the Americans with the exception of a very small run of high quality H & R shotguns so rare as to be rarely seen.
There aren’t “K” grade steel barrels. K grade stamped on the barrels refers to the grade of gun. The barrels are either Damascus (by far the most common on 1900, at least that I have run across) or Remington steel.
The different versions of a 1900 were (steel was cheaper than Damascus).
K - Remington steel, extractors
KE - Remington steel ejectors
KD - Damascus, extractors
KED - Damascus ejectors.
You gun was likely made in 1903 and is the lowest priced version of a K grade. Retail in 1903 would have been $35.