So, it looks like your options are as follows:
1. Bad public school in dangerous distant neighborhood that's part of a hostile-to-gifted system. Okay, cross that one off.
2. Dodgey private school that some people like and some don't.
3. Homeschool (if you both work and/or you don't like that idea cross that one off).
4. Other (small boutique school). This will require going page-by-page through a copy of Bay Area Parent Schools Edition (possibly online, possibly on the newstands) and scrutinizing each ad.
It sounds to me like you need to choose between options 2 or 4.
FWIW, I wouldn't recommend Stratford. We looked at it for my daughter and heard bad things about it: high pressure, super-competitive, that kind of thing. Stratford isn't supportive of acceleration (at least, they weren't with my daughter; I asked about moving her up a year in math, and the principal (!) told me that she'd have to talk to corporate about that. If a principal can't make such a basic decision, that's a bad sign. And I had to talk to her because the math teacher pretty much gagged when I asked him ("Oh! That's not MY decision! You'd have to talk to the principal!").
There are small schools out there, but you may have to dig to find them. You may also have to accept that they'll only work for a while.
San Francisco isn't known for having a kid-friendly atmosphere in general (people have been complaining about this problem, and especially that whole school-lottery thing, for many years).
