Do you mean brushed or bead-blasted? My 1076 is bead-blasted, aka matte finish. Brushed finish is what you get with a fine-grit abrasive belt. and is typified by parallel scratches. Brushed finish usually winds up on slide flats as a shinier accent to blued or matte finishes.
The point of this distinction is that bead-blasting can be polished off with a buffing wheel, whereas brushed finish has fairly deep scratches, which will require real work to remove. If you polish brushed finish, you're left with a "scratched mirror" look, with shiny metal interspersed with burnished scratches. Bead-blast finish can leave pits behind in the same way if the blast abrasive was fairly coarse.
Most brush finishes are in the realm of 220-320 grit abrasive. If you have to remove such scratches, you're looking at removing a couple of thousandths of material over several square inches. This is best accomplished with sequentially finer grits of emery cloth and sand paper. Each polishing step must be thorough, so as to remove all the scratches from the coarser grits. This gets tricky down at the finer (400-600) levels, and it's frustrating to find scrathes that won't polish out when you're trying to change to the next grit. Spot-polishing particularly deep marks does not pay off, as you will dig dips in the surface. Mirror finishes reveal even the slightest flaws or dips in the surface. Once you get down to 600 grit, you can move to buffing.
Try a buffing wheel and Jewler's rouge or Simichrome. You can get different grits of rouge at lapidary supply stores. For tight spots, the hard felt wheels for Dremel tools are just the ticket.
BE CAREFUL WITH THE BUFFING WHEEL! You can easily dig "waves" into the surfaces that want to be flat. Even the finest polishes can do this with the help of the wheel. Polishing out mistakes of this type gualifies as sweaty gruntwork. Of course, the real fix is to go get the coarse grit and start over.
Large flats can be polished with sanding blocks to avoid dips. I like to use hardwood blocks with a layer of sheet rubber, like a bicycle inner tube, applied with spray adhesive.
I got out my 1076 and looked at it. Realistically, this is HOURS of work. If you think your time is worth anything, look into handing the task off to a professional. A sloppily done polishing job can look terrible. Mirror finish is absolutely unforgiving. Think of the finish on cheap nickle-plated automatics...
I learned all this the hard way, making high-vacuum mass-spectrometer manifolds out of stainless steel for Hewlett-Packard. The people working in their Q-A department were VERY picky, and enjoyed rejecting entire batches of assemblies if they found one tiny little flaw.
I hope this helps. You're looking at a labor-intensive, messy sweaty job. (That black stuff gets everywhere, and it's hard to wash off.) Gun manufacturers look at polishing as skilled labor, so perhaps it is not casually done, unless you have copious amounts of the patience it takes to get the job done right.
Of course, you don't HAVE to be as persnickity about it as me...
Do a web serch on "Stainless Polishing" and your going to get many hits on suppliers.