I read once how to make a shiny plate looked brushed. Don't remember if it was stainless or not, but it sticks in my mind that it was. They took the piece they wanted to "brush" and clamped it to a workbench top with a straight edge. Then they took a sanding block loaded with fairly coarse sandpaper and simply pushed it back and forth along the straight-edge (so the brush marks were parallel) Then they moved the straight-edge and re-clamped it and finished the sanding.
I've never tried it, but is seems pretty easy and the sanding might give just a bit of "grip" when stepping on it.
Craig