What about going deeper and wider instead of accelerating? What I mean is, instead of going on to the next "grade level" math or whatever, go into more depth on math concepts that don't typically get covered in regular math (don't know enough math to give examples). Or, focus on World War I instead of going with the "world history". Science has endless possibilites that don't get covered in regular school. That way, he learns stuff but isn't so far ahead of his age mates in the regular school curriculum.
Or, is this what the Independent Studies teacher is doing?