Oh, I wanted to add: It can help to go to schools asking for their help. People like to help. Tell them that the situation is that your child has scored very well on the WPPSI and that you believe that she is already working past K level. Ask them if it is possible for a K teacher to pull kids out for differentiated instruction in all the different subjects in which she is ahead (it usually isn't). Ask them what solutions they would have in such a situation to make sure that your child was advancing in all areas throughout the year. If you have any anecdotal evidence of social maturity, make them aware of that as that is often of primary concern for school administrators.
BTW: I think asking about starting K mid-year is at least worth trying. It makes sense to me since that is close to where she is academically and she would have a few months to learn how to go to school and it would make the transition to 1st smoother, thus alleviating some of the school's concerns about social issues.
