Need help resolving a 1903's insufficient headspace

[browningautorifle]

If there is no barrel shoulder

There should be a shoulder. I can't picture a military barrel without one, nor a civilian barrel presently. If no shoulder then it would turn against a ring inside the receiver, or like the Lee Enfield, both.

it would not take much rotation to set the barrel head back quite a bit

When you talk about setback, you talk about it in a complete rotation, usually. If it were certain civilian rifles with rapid taper and unmarked barrels you could get away with less. It takes a minute to figure out how much to machine off the shoulder to give one turn to TDC.

Ive ruined a number of barrels when I cut the chamber too deep

You wouldn't be alone. Very, very careful. Last M1 rifle I did was a .308 barrel and it took so long with a breech end ream...but turned out perfect and tight.

Information

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[SkyKid]

Maybe you are thinking about peening or rolling the receiver to move the metal forward which is common practice
I've done this when the witness mark on the barrel goes beyond the receiver mark

[browningautorifle]

peening or rolling the receiver to move the metal forward which is common practice

That's done if the barrel goes past TDC and you need some metal, or an older barrel that has already had the crush factor used when it was installed. I had a 742 Remington in .308 come in that had excess headspace and I set the barrel back one turn to correct it...worked perfectly. But that's not what's needed here, this one just needs a touch of reaming.

[RDG]

From this and other sources I agree that a bit of reaming should help, but I have never reamed a gun and do not plan to start now. Plus, I think I want a Hatcher hole drilled and the extractor to have a hole drilled to match the gas escape hole on the right side of the receiver just like my other 1903 has.

[Garandy]

If you are mechanically inclined and don't feel like buying one, chamber reamers can be rented.

[ssgross]

I cannot close the bolt on the Go gauge

Before you do anything permanent, clean, clean, and clean the chamber again. Scrub and scrub some more. Stuff some patches soaked in kerosene into the chamber and let it soak, and scrub again. If your rifle has sat for that long, dried oil and grease will affect the reading on your gauge. How do I know? Same thing happened to me. I bought a beautiful Remington 1903. It had a sedgly replacement barrel on it. After thorough cleaning, wouldn't close on a go gauge. I thought short chambered just like others have said. So I chased with a reamer. I pulled out after a couple gentle turns followed by just one good one, since I new I would just need to kiss it if at all to get the bolt to drop. The swarf that came out had no metal on it...just crusty dark brown gunk (not orange/red like rust would be). Closed on the go gauge immediately.

If you've ever disassembled, say a winchester 97 or worse a model 12, which most owners in it's history are too timid to disassemble and really clean, you'll know that decades old grease or oil will cement with dust, fouling, etc. and create a near impenetrable mess. I had a model 12 once that not even a week long soak in kerosene would lift out all the cement from behind the bolt. As a last resort...boiling in water will lift it out, or make it brittle enough to come off with a good scrubbing.

EDIT: if you indeed do have a short chamber, the bolt will not close at all on round (remove all fire control before checking). If it's just old and dirty, the bolt will likely gently squeeze shut on some rounds. Short chambered barrels are like 0.010 short or sometimes more. I've fit some NOS 1903 barrels still in the grease and this was the case. If it's short, your bolt won't come anywhere near closing. You wouldn't even be able to pound it shut with a hammer on round. Post a picture of where your bolt is falling.

[RossMkIIEnjoyer]

There is a reamer you can get called a pull through finish reamer get that has a rod attached that runs through the end of the barrel I've seen used. Seemed like a relatively simple job. They're not too expensive and can be resold when finished. Cheaper than a gunsmith. Or just a good excuse to get more tools.
This guy uses one at 21:45:

[ssgross]

pull through finish reamer

If you do end up needing it, you can rent reamers affordably from https://4drentals.com. I have used them several times before.
A pull through reamer would work, but is really designed for actions like m1 garand or carbine where the rear is closed. You can rent a t-handle from 4d with the reamer for your 1903. The first time I reamed a chamber I wrapped vinyl tape around the shank of the handle to help keep it centered in the action. I quickly learned it wasn't needed. If you are patient and go slow, things will turn out perfect. It is very very easy to do. Larry mr. Potterfield shows off how easy it is... he reams at 3:20.

[ArtPahl]

Somebody has to say it: Since it's a low number, shouldn't shoot it anyway.

[RossMkIIEnjoyer]

A pull through reamer would work, but is really designed for actions like m1 garand or carbine where the rear is closed. You can rent a t-handle from 4d with the reamer for your 1903. The first time I reamed a chamber I wrapped vinyl tape around the shank of the handle to help keep it centered in the action. I quickly learned it wasn't needed. If you are patient and go slow, things will turn out perfect. It is very very easy to do. Larry mr. Potterfield shows off how easy it is... he reams at 3:20.

Huh. Thanks. Never seen finish reaming with a t-handle. Or maybe I forgot? Had it in my head the barrel was to be pulled and finished in a lathe but the pull through reamer was a work around. Probably gotten that conflated with finishing barrels like for ar15s. That'd be why I keep my books and read again before starting a new project.