New to me Rock Island 1903 with strange marking

Hi all, first post but been looking for some time. Great forum with a fantastic amount of information. I wonder if you could help me with some markings on this rifle?Attachment 89958Attachment 89959

Plus more pictures. There is no NS mark on the bolt. The single gas port is the same size as the one in the extractor. No Hatcher hole. There is a H stamped under the bayo lug. No cartouches I can see on the stock. There is a W3L on the bolt handle stub. Any information is appreciated. I understand that this rifle was made in 1919 as the serial number is 338524. Barrel was replaced in January 1931 at Springfield Armoury. What is the significance of the W mark infront of the mag well?

Bear with me as this technology thing is above my retirement pay level..

Gonna need a nap after this effort..

First the good news. It's a high serial numbered rifle. Means you can shoot it as much as you like.
Not seeing a 'W' anywhere, but I suspect that's not an issue stamp anyway. Might be a Unit thing or put there by some previous owner. Could even be a State National Guard or prison use stamp.
Rummage around here. Clicking on 'Manufacture Dates' could cause you to go to bed, pull the covers over your head and stay there until Spring. snicker.
U.S. Rifle Modle of 1903

i would look at vishooters 1903 page for better info on serial numbers,
never seen that W before,
bolt is a WLK3 springfield bolt. barrel is also likely a SA replacement