Be VERY careful with that Magic Eraser. Very easy to scrub right through the paint to bare wood.

My advice: Get all the gunk off of the pf that is there right now (using novus or whatnot), apply some wax, and play it! You can use a Magic Eraser to get out some ball swirls and ground in dirt from cracks, but it is not a miracle tool that will make it shine like a brand new clear coated PF.

op... always remember... the enemy of "good enough" is "better"...

judicious use of magic erasers can get you to "good enough"...

non-judicious use will definitely result in "not better"...

After using ME and alcohol and when I get too nervous to use it anymore, I've had good luck using an auto clay bar with lubricate.
http://www.autogeek.net/detailing-clay-bar.html

I would not use this on non-clearcoated PFs.

I primarily work on early SS Bally/Stern games with lacquer finishes and never had a problem. I can't speak to the Williams games. Here is a before and after pic of a Xenon PF I am working on. I started with ME and alcohol and finished with clay.
Xenon before after.PNG

it works fine on non clearcoated fields, but your never going to get all the swirls out. With taxi it's ground in so hardcore, your going to have a hard time getting it out. When I do taxis, I do it until the gray gets light, and that's about as far as you can go. IT's not going to be perfect. There is no way to get ball swirls out of light colors 100%.

Chemical cleaning & reconditioning