Being that I'm still nervous to try the silver cleaner on my stone (without damaging the metal) I decided to try the electric toothbrush/paste method first.
After 2 cycles with my electric toothpaste and some Crest Whiten Toothpaste it took approx. 95% of the "smudges" away!! I'm so excited! I'll try another cycle tonight to see if I can get the remainder of the smudges off, but as of now it appears to have worked. I guess whitening toothpaste is not just for your teeth!
Thank you to everyone for the great suggestions!