All this is way to much work.
Never use anything on a rag. You'll get super dull and nothing. It looks awfull.
You can use 4-0 steel wool between coats, but not to finish. Carefull. l
Use either fine pumice and oil or rottenstone and oil on a toothbrush. Scrub it and wipe it off with a soft teeshirt. The pumice is more aggressive and thus duller. I use rottenstone most of the time. Using water instead of the oil is even more aggressive. Just never use a rag to apply it. Tooth brush or any stiff brush.
Finally finish with one last coat that is wiped off or a little wax.
OH - MY Bill say it an't so -- you will now get the "Rath of Dan" on you!!!
Rath was a meat packing plant in Waterloo, Iowa
People learn what works for THEM in wood finishing in many cases.
I have learned that some batches of linseed oil seem to require reheating if they get old to restore their drying properties. I don't know why but it SEEMS to be the case. Could be what was added and how it was processed. The actual level or type of dryer used buy the company that made the base oil. The problem is that it takes sometimes a lot of time to figure some of these things out. Most store bought finishes are made for "shine" few are really suitable for firearms in the long term. Other than spirit varnish traditional oil based finishes will develop more shine with use.
I am fairly certain that a scraped finish that many here like can be smoothed with a coat of a heavy bodied varnish that would cover the scraper marks in one coat something that a modern varnish that is only 20 to 40% solids just cannot do. this excess of solvents allows the varnish to be more user friendly for someone refinishing a chair or table. They flatten almost instantly and leave a nice shine unless a "low gloss" version. The ability to flatten to a smooth surface makes it easier for them to shine.
A heavy bodied oil with a relatively slow drying time will often not flatten completely. It make retain some brush marks or even the ridges of the skin of the person that applied it if its spread with the hand. These can often be seen on oil varnish on rifles that still have all their finish. But these are generally late 19th c BL rifles like Ballards and it will require magnification to show them. Also these will tend to wear down and make for a glossier finish over time.
These thick bodied varnishes will not penetrate well. This speeds the finishing time and may only require on coat. High solvent content finishes will not do this they lack enough solids to cover the wood in one coat and since they are so thin they penetrate bare wood and will produce "dry spots" for the first couple of coats. Thin finishes with a lot of stoddard solvent or what ever will dry fast but they require far too many coats to get a finish. If its a scraped finish it may take even longer. The more times that a stock is touched to apply finish the more opportunity for "problems". I used to do a lot of wet sanding on Walnut. Its something that a Drill Instructor could use for punishment in Boot Camp. But lots of people seem to like all that work. I don't . Curly hard maple can be finished in one or two coats. A HUNTING rifle can be coated with a turpentine thinned oil, allowed to soak in for a few minutes, wiped dry, assembled and hunted with immediately. This will give a dull finish but it will be pretty durable and protective and in a week of so will start to show some increased shine where the users hands rub on it on use. Better penetration can be achieved by heating the wood before application and after with radiant heat. I would think that this would be perfect for a SMR and would not be too surprised to find many had a similar one coat finish applied. It is cheap and very effective for a "service" rifle type finish.
Dan