DD did that to my stone hearth, so you aren't alone in this experience.
I tried all the same things you did (my favorite was trying the Magic Eraser and having it just shred to pieces), including scrubbing with an old toothbrush. My hearth is real stone though (at least I think it is, I could be wrong). What finally worked for me was using Soft Scrub, super fine steel wool, and a lot of scrubbing. It finally worked, except for a couple of crevices that I just couldn't get into - but I can't tell anymore where they were, so I must have gotten used to it or they dissapeared on their own. The bad part about that is that it was a huge mess to do it and then I had to clean off the Soft Scrub and steel wool afterwards which was a big pain. I just used rags and water to wipe it all off. If you try it, put lots and lots of towels underneath. Otherwise, I like some of the other ideas you've been given. They might do the trick while being less messy and easier to do compaired to what I did.