Congrats on getting your gut instincts confirmed. As far as schooling goes, we've had mixed success with public schools, private school and homeschooling. (Yes, we've tried them all wink ) While our public/private school experiences were very similar, our charter school actually ended up being the best - even better than homeschooling.
Homeschooling didn't work for us because DD3 at the time was too much of a distraction from DD7 at the time getting anything productive done. The younger one was very time intensive and high demanding child, (Luckily she has grown out of that). The older daughter, the one we were trying to homeschool is also a very social child and didn't like learning alone. We were not in an area with good homeschool groups for her age/ability levels, so we couldn't join one for her social needs to be met.
Both the public and private schools tried to help accommodate her, but they both reached limits to what they were able/willing to do. Even with radical acceleration from grade 3 to grade 6, she wasn't getting what she needed.
We have since moved so she can attend the Davidson academy and it has been an awesome fit in all ways for her.
Good luck with your journey. But don't plan too far in advance, because what works now will probably not work next year, or even in a few months. I think flexibility is key to success in educating our kids.