Your child sounds a lot like my 9 year old. He is in his school's Gifted and Talented Program, but it's only once a week, and it's just not enough.
With a little research we have found a (tuition free) elementary school especially geared towards Gifted and Talented students, and we applied for it. We missed the deadline, so for right now he's on the waiting list. I really hope he will get in.
I really don't have any actual advice, as we are still dealing with the issues that come with having a bright child too. My son is also bipolar (his pdoc says he's bipolar, but officially he calls it Mood Disorder NOS, because of his age), which doesn't help. Luckily his teacher is an angel, and really tries to work with him, but she's clearly in over her head.
Good luck, I hope you can figure out something.