Grinding melted latex off a pizza stone?

It won't suffer much from having a millimeter or two of material removed in one area, so I'd just go ahead with the Dremel and grind it down to clean stone rather than resorting to chemicals that may or may not work and may or may not impregnate the stone. There's no substance made short of diamonds that can resist a grinding wheel. Worst case is you end up with one side that's unusable for anything that requires a smooth surface, but otherwise it should be fine. It's mainly just a rock, after all.

Silkscreening ink is made to withstand scratching. So I wouldn't go the dremel route.

The first I would try to do is to transfer it again somewhere else, to something more porous/sticky than the pizza stone. The best thing would probably be blotting paper, if you can get it, but if not, try other types of non-glossy paper. Heat the stone again, then put the new material on it and press strong enough. A hot clothesiron above the new material might work best - it could be worthwhile trying it with a cold stone and a hot iron, meaning that the latex is hot (therefore sticky) on the paper side but not on the stone side.

If that doesn't work, I would try to get it off by a chemical process, throwing ever stronger acids, bases and solvents on it until something works. Even though other cooks dislike the idea, I haven't seen any sticky film capable of withstanding concentrated NaOH (I have used it to remove seasoning from polished forged iron, which did not go off by dremel), and the stone (provided it is natural stone) shouldn't suffer. Of course, this should be the last step - vinegar, baking soda, bleach, concentrated ethanol and maybe acetone-free nail polish remover should come first (do not mix any two at once!).

If your experience is anything like mine the pizza stone won't survive long enough to bother maintaining it. Maybe I need to find a thicker stone, but the three we've bought so far have all cracked through normal (even light) use.

That said, if your pizza stone is worth the effort, I'd recommend a "burn it off" approach vs an orbital sander.

Do you have a BBQ?

Place the pizza stone in there (latex-side down), close the lid, and turn it up to full blast (toss some foil-wrapped potatoes or something there while you're at it). An episode of Pitmasters later, and you'll likely have burned off most of the residue without risk of melting it further into the surface. Don't open it until completely cooled. The somewhat-even heating and cooling will mitigates the risk of cracking it. You can probably try this in an oven, but a decent BBQ will get much hotter.

You wont likely have a shiny-new stone after the scorching; but hey, a well-used stone wont stay pristine for all that long anyway.