I am not expert in education - but I see a child who wants to learn more, is SUPER well behaved, has shown consistently he excels in math - WHY DENY him ?
luvedu, your son's story closely parallels my son's. My son is younger at 6, but your post bought a sense of deja vu to me. I too have problems with "afterschooling" for hours upon hours in my son's areas of strengths. I find it counter intuitive and counter productive. But, I live in an area where it is the norm rather than the exception.
Some strategies that might help:
1. Use online programs (EPGY online is an example) and the Great Courses DVDs as enrichment tools. Your son can learn at his convenience.
2. Try to get your son a mentor or a tutor in advanced math - I have a strong math background and teach my son now, but, I would like him to have a mentor to guide him later on.
3. Enter your son in a Math olympiad or Math Kangaroo like competition - if your son wins a significant prize, the school has to acknowledge that he is gifted in math, right???
4. Please consider enrolling your son into your local Math Circle. The advantage is that your son can interact with like minded peers, advance significantly in math and will have a mentor to guide him.
In addition to these, I have a curriculum that is good that I use to teach my son at home.
I am sorry that your son's gifted school thinks that they are "experts" in teaching your son. If they say that you should look for another school, then, maybe you should ... because in addition to fee, you are paying them a donation too!
Good luck with the DYS application. Maybe they will help you find a solution.