You're probably not going to get that Browning finish off with just acetone. You might try carb or brake cleaner, with a combination of solvents.
You might get some scrapers (or use a safety razor) to scrape softened finish off the stock.
Agree with Scorch - don't use steel wool. Until you have the grain filled, you can end up with steel wool pieces in the pores of the wood, which will rust or look like crap when you're done.
Use some backing when sanding to maintain edges.
BTW, when repairing scratches on Browning finishes, I soften the edge of the nick or scratch, then use some Pro Custom Oil, then allow it to dry. Then I sand down the PCO patch with 400 grit, then 600 grit. Apply a second coat, try to make it blend into the surrounding finish. Let the second coat dry and harden well - maybe put a heating source over it to accelerate this.
Wet sand with 600, then 800. Then get some 3F, then 5F rubbing compound and shine up the area. After you're done, you can't see where the scratch/nick was if you get it right. I use this technique all the time on Brownings that have nicks/scratches in that high-gloss finish.