I had the opportunity to do some refinishing on an M1 Carbine recently.
Yours looks a bit more aged than the one I worked on; the difference being the darkening of the old wood finish. That's a typical effect resulting from age and the effects where handling contaminates the Linseed Oil with Gun oil.
I cleaned the wood with alcohol to loosen any gun oil residue, and followed up with OMS (Odorless Mineral Spirits) to loosen up the old BLO (Boiled Linseed Oil) that eventually ends up being used on wooden military rifle stocks in civilian hands. Nothing wrong with BLO, it's what I also choose to employ.
After the loosening comes the steel wool. The aged goop need to come off and dawdling doesn't help. I used #3 Grade to begin with. Technique is crucial here; don't let yourself cut away the contours of the wood, especially the ridges and corners. The process is best described as surgical removal. Once the surfaces are free of the main accumulation; put the #3 Grade away and leave it there. What you should have should look like well aged wood with traces of an older finish.
Take O Grade steel wool and gently improve the texture of the remaining surface finish. It should develop the hint of some sheen. Give it another soak and vigorously wipe down with Rubbing Alcohol and Odorless Mineral Spirits. I use the bundled terry bar cloths from Costco. Let it thoroughly dry, then thin out a few ounces of BLO with an equal part of OMS.
Apply the finish mix with a fingerful dotted onto the wood, then rubbed in with the palm. Rub hard, generating friction heat, spreading the dots to fully cover the surface. The heat and friction drives the finish deeper into the wood, creating an durable bond between the mixture and fibrous structure of the wood itself. It also ensures that there is no overload, creating runs and other gack. The goal is to build the finish
into the wood, and not atop it. The mixture must be allowed to dry to hardness before applying the next coat. A couple or three coats, hardened; and the next grade of Steel wool (000 or 0000) becomes the polishing medium. Still paying attention to not wear down the ridges and corners; polish the surface until the entire surface is down to the wood grain again. Do this process a few times.
By now, the sheen is building up. What's occurring is that the top finish is getting repeatedly cut away, but the recessed grain is also filling up. The finish will pop when the filled grain and the cut down surface reach the same level.
At this point, a decision needs to be made; Glossy or Satin?
If Satin, one thin coat over the polished down wood surface, harden; done. This is what I think of as a Combat Finish. Classy, but not gleaming so it attracts the wrong kind of attention in the field.
Glossy, another thin coat, hand rubbed vigorously, hardened, and maybe a repeat. That should knock your eye out. This is the Ceremonial Parade Rifle finish; not unlike what you'd see at Arlington.
Over time; the finish may dull and/or darken. No worry; clean with Rubbing Alcohol and repeat the final cut down, recoat process.
Some things can contaminate and ruin this repairability feature of the process. Silicone is no good for these finishes, making it very difficult to get a repair coating to stick properly in a process similar to where silicone contamination causes 'fish eye' in automotive coatings. Urethane looks wonderful; but it may not be repairable without a complete strip. The stuff left in the grain may not allow BLO to be used to replace it again; it may not stick properly.
For the metal, my process is to degrease and clean using the same Rubbing Alcohol and OMS agents. Once clean, handle without fingerprints, and apply
Brownell's 44-40 Creme Gun Blue. It works near instantly, but I leave it on until it wants to dry up. I then remove it with Rubbing Alcohol, drying it and immediately following up with a quality gun oil; I use
Lucas Extreme Duty Gun Oil. Wash hands well and moisturize after getting the Blueing compound on the skin; Nitrile Gloves may be a good idea. The 44-40 is great stuff, it results in deep black finish.
I have the supreme pleasure of maintaining our VFW Post's eight Ceremonial Parade Garands. This process is the same one I use on them.
Greg