Scotchbrite Pads
Hi, I'm a new member and this is my first post but I thought I'd jump in. I used to work at a bus manufacturing plant where they used the green houshold type scotchbrite pads for taking scratches out of stainless steel panels which had been scratched. It only worked for light surface scratches, not gouges. The scotchbrite in turn left it's own lighter scratches in the surface but the panels were intended to have a light brushed appearance. I'm told there are other, finer grades of scotchbrite of gray color available from industrial supply houses but there may be additional grades also.
I would expect the scotchbrite to leave a more scratched appearance than you want. Perhaps 0000 steel wool with an oil after you have used a blueing remover would be better.
Good luck in your project.