I've done a little research and If I have the material correct, there may not be a way to polish Arborite. Arborite is a high pressure plastic laminate. This isn't something I'm sure of, but I think that what you have is similar to Formica. One of the weaknesses of this type of counter top is that when they're worn out, there really is no way to restore them.
Thats just my opinion, others here may know something I don't.