It sounds like the principal will be hard to convince re a full skip. Would the school consider letting her go to 1st (or 2nd) grade for math? This is the area where she clearly needs acceleration according to their own tests. If it goes well, then you may be able to convince them to let her go there for other subjects?

Keep working on it. My DS had a difficult year in K last year due to boredom. It only got worse as the year went on.