I second the Dremel/rotary tool; you can also use a belt sander, though for something of THAT size, it might be too tricky! Cutting the edge down beforehand to get that taper will save you a lot of time and dust when sanding.
In regards to the foam clay, the issue is probably that it isn't as durable as normal foam. It's a lot softer than EVA foam and the thicker it is, the longer it takes to dry too. What are you trying to do with the clay?