We were in a similar spot three years ago -- ds was even taking Saturday classes at CTD, we lived in Evanston! My ds-then-5 had even higher MAP scores, and his school flat-out denied a skip. Wouldn't do it. We had him privately tested and they blew off the results.
It was beyond frustrating, and we ended up moving him to one of the massively over-priced private GT schools in the area (which we really can't afford).
If I had it to do over again, I'd have gone above the principal's head when it became clear I wasn't getting anywhere with her. She was a brick wall.
There is some truth to the idea that if you skip her, you still want her to be top of the class in the *new* grade. Looking at her scores, I think she'd probably be well-placed in second grade next year.
If you feel a skip would be best for her, stick to your guns, and don't be afraid to escalate! I know that's not a ton of help, but I took the easy way out of the situation. :-/
