Hi J.,
I have two children who are in public school, my oldest has had nothing but trouble getting into the school of our choice.
Both times I have appealed and received a reply in June (elementary) and in September (middle school). For a while my son was unassigned, we ended up sending him to a private school in a K-8 school for middle school. It's one of the cheaper schools and he received a wonderful education. Perhaps you can send your child there for a year and try again next year?
The 10 day count is nerve racking but a gamble.
It really depends on the school you are waiting for, all the private schools have asked for their money up front so there shouldn't be any movement there. Usually the secretary or the principle knows what is going on (some parents who have not replied or may be moving soon, but registered their child anyway). If you know an active parent in that school, you may get the inside low down from them.
Good luck, it's by far the ugly side of SF school process. I know there will be movement in the school board soon, you should voice your disgust! I am!
Best of luck, I really do feel your pain
T.