One more thought. Mostly, It's been my experience that administrators are very hesitant to grade skip or subject skip out of concern for the student. They want to be very confident the child will still do well if accelerated.
Perhaps you could borrow your friends' textbook and do some work out of it and then present it to your math chair. I can't guarantee it would convince him to accelerate you, but it might be worth a try. If nothing else, he will see that you are serious about your wish to have more appropriate math challenges at school.
