I think the engine turning, or guilloché, is quite beautiful and Paul's machines look great finished that way. This is one of Paul's images (borrowed without specific permission) for illustrative purposes.
I searched for companies that polish stainless steel in Salt Lake and I don't know if I used the wrong terminology or perhaps there just aren't many places here that do this work but came up with very little. Finally after checking with some friends I was sent to Quality Plating. Their specialty is plating, of course, but they have a guy polishing as well. They can only do simple polishing and the parts I had done came out very nice. It was not cheap. I could replace a boiler for the money it will cost to have the whole machine polished. I think I'm going to go to Home Depot and try the sandpaper method Greg outlined. I could then at least finish the top covers with the same look.
The money is going to go to some home renovation work so when this Linea is finally complete it will have a proper home.