Hi, Cee. We have been there, and so I sympathize with your dilemma. We left public school at the beginning of 5th grade in similar circumstances -- gifted pianist in a sports culture, public school concentrating resources on kids not able to pass the MCAS (Massachusetts NCLB test), and so on. The last straw was when the math agenda for the year was announced to be: "Let's be sure everyone knows their math facts!" My child was bored and frustrated, ready for pre-algebra but stuck in arithmetic -- ready for Shakespeare but stuck with Jerry Spinelli.
We had the same issue with local private schools. The pressure level is high, and they have mandatory (!) team sports. The model is that the kids get on the bus at 7 am and come home at 7 pm. It's a full-service model, but it didn't fit us (let alone the price tag of $30K+): the sports are (for us) not wanted, and the music offerings are often not strong, compared to our network of private teachers and regional orchestras -- so we don't need the school-based extras.
I homeschooled for the first two years. Then we found a gifted online program that works for us: it's distance learning that is geared to gifted kids (the school will let the kids accelerate to any degree and will customize content to enrich it). My kid took 9th grade Honors English (the Odyssey, Romeo and Juliet, lots of literary analysis and a number of 1500-word essays) in 7th grade and has never looked back. High-school Algebra in 7th grade was a good fit, too. The teachers, in our experience, "get" gifted kids -- the English teacher says she has elementary students reading and comprehending at the college level.
Caveats: Be careful with online schools. We tried a couple, and some of them are not good. There are terrible, computer-based curricula based on multi-choice work, and some of the schools put enormous time pressure on teachers, even prohibiting feedback! Our school is more expensive, has a longer history of distance learning, does not use multi-choice much, and has a special gifted division. Even so, our online school requires a lot of parental time (unless you hire tutors): the teachers are there to review and give high-level comments, not dig into every comma or discuss every reading. And, as with homeschooling, you have to deal with the social question, which isn't easy. My kid is in an orchestra (cello now) and takes a ton of music classes with others; also classes through our local library and language school.
So it isn't cheap or easy but it works for us. Good luck with your choice. I am sure others will offer alternatives too.