You want that sheen on the outside of the slide? I'd start with paint finishing materials. House of color ca link up to fine sand papers. Or auto parts store. Try swirl mark remover, or 3M's 3 step process from scratch out to glaze. iT there are two many scratches. work the from the finest if not enough use a slightly courser. Say 2000 grit first. If not enough 1500 then 2000. still scratches go to 1200 grit, 1500 2000 swirl mark glaze.
It is possible to get a mirror finish on stainless steel you just don't want to start with a very course sandpaper and remove the 27/7 and other light stampings. The serial numbers are much deeper and will need a grinder to remove.
It takes time but is possible to get a mirror finish without removing any of the stamping.
Go slow, take your time, give your arm a good workout.
