Now I do and is the same on my 1903-A3 stock.
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Not a "few" were bad. Actually production was quite consistent and almost all were over-heated in the Forge House. Use moderate hand loads with new brass. Good luck.
Far as price goes, that serial number is a swift kick to the groin. On low number actions as long as the rest of the rifle is period correct they have collector value and can fetch a decent price. Not the case with yours when it's a mix matched rifle on top of a LN receiver. In your case it's only worth what the parts are worth and in those regards odds are greater it was not an arsenal product, specially with no arsenal marks on the stock (which itself could have been changed too). Not saying it's not arsenal built but to this day NOS HS barrels are still on the market so anyone could have built this rifle, does it have a Hatcher hole?
The stock does have provision for A3 HG retaining ring but could would need to see pics of the left side to tell manufacturer? I guess while I'm delivering bad news... it was Steve McQueen and I too like that movie, love the shots of them/ him using the 03. I like the fact that despite Hollywood's usual shortcuts he actually uses the rifle correctly, flipping the sight up and adjusting to take the shot on Po-Han.
Oh yeh, I was wondering if someone would catch that! Good job. Now I know that I'm not the only one who was a fan! LoL Glad I only paid $225 for this miserable piece of of parts on a knawed out log! Guy said he carried it around all day, at the gun show, and was tired and wanted to go home. He's happy, I'm happy so all is good in the world.