Remington 1903A1 C stock?

[Sheriff]

Hi everybody, I am a brand new member, you guys are great. I need help narrowing down and identifing a gun my father has had for a long time. On the reciever it says (US Remington model 1903 31670XX) The reciever is flat under the sight but does not have the two flat milled areas to either side of the sight, but is radiused there. There is one hole on one side and a larger hole on the other side. The steel is not parkerized. The rear ladder sight is missing, but there is a Redfield peepe hole style sight at the far rear over the back of the bolt that is highly adjustable. The barrel is marked (R A flaming bomb 7-42) it is a 4 groove and does not have a star guage stamp on the end of muzle. It also has a P in a sqare box. The floor plate is milled not stamped. The stock is a pistol grip C stock and the only marking we can find is a P in a box. The butt plate is not a Remington model and has no date stamp on the inside of it. The cut off lever has a (B) the safety switch has a (R) the bolt has (R) and also a 17 in a circle and also a 1 in a sqare box. Your guys input would be greatly appreciated, Thanks.