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No one knows what many of the barrel markings mean. From the info you provided the ///KG3 should mean that you have a Model 1900 K grade which has Remington steel barrels and extractors. There is some thought that /// refers to degree of choke but with the pellet counts stamped on the lugs this seems unnecessary. Remington was fairly consistent stamping some form of the K's, E's & D's on the barrels but the other letters and symbols are a mystery. For more details you may want to consult Semmer's book Remington Double Shotguns.
BTW - your gun left the factory in early to mid 1902.
I thought your S/N looked like it might be close to one I own (320187). A bit farther than I thought but it bears barrel stampings of (star)KG3. Close but no cigar.
Couple more details -- the lugs on the 32" barrels are stamped 46 & 55 indicating imp. modified for both.
Maybe /// & (star) denote barrel length??????? What length are your barrels? Lug stampings?
I love the old girl! Being a short chambered gun, I've always shot PolyWad Vintager shells thru it. It's a wee bit short on the stock (I'm 6'5" and have long ape arms... lol!), so I'm going to find a repo or used buttplate to thin down as a "spacer" then affix a pad to lengthen it just a bit.
The gun belonged to my great-Grandpa and was given to me by my Grandpa years ago. My boys will be ready to use it anytime now.
A bit about chamber length. Maybe Researcher can add his input.
A theory that may have been held at the time by Parker and Fox was to utilize a chamber length of 2 5/8" which would provide a better gas seal in the forcing cone when the crimp from a 2 3/4" case unrolled which, in turn, would result in better patterns. There is no evidence I know of that Remington held this view.
In any event - I along with others use 2 3/4" cases while keeping pressure at or below 5000 psi or so. On the other hand some have reamed the chambers to 2 3/4".