The table looks like it was shellacked, try a bit of alcohol in an iconspicuous area. That may clean it up. Rottestone may clean up the top. It will clean, polish and oil at the same time.
Striping the orignal finish may take some of the value away from the cabinet
You can also try Fromby's (or another brand) refinisher. It will leave the original finish.
If the white isn't very deep try toothpaste with the Mr Clean Eraser.
I know to clean a painting I was told to use spit on a cotton swab, you may try that on the gold.
Anything you try, start where it can't be seen in case it does more damage.
It's a beautiful machine.