Instead of salt and baking soda try:
Calgon water softener and Arm and Hammer washing soda,
or
Raindrops water softener
or
Arm and Hammer Fabricare in powder form.
Special Metal Cleaners, Inc. - Cleaning Silver Made Easy This is an aluminum plate and instructions.
You can also use a piece of aluminum extrusion or plate from your Home Depot or Lowes or hardware store. Raw Aluminum works the best.