I'm just the "mom" with the public school list, but I am pinging the teachers to see if they can help with any further suggestions.
There are just so many dynamics that could be at play here. In my case it was at the district level, because the school level was putting my daughter in classes above her grade level --- until some parents complained and the principal was told those programs were to end.
It sounds as if the district *could* do this, if the right person were contacted, but it does sometimes depend upon the state and the district. Some states allow students to skip grades, for instance, and others do not.
Also, as has been mentioned, in some states, gifted is considered special education, and gifted students must be given an “appropriate” education just as those with developmental or learning problems must be.
In our state, high school juniors and seniors may take college courses instead of high school courses, and the state pays for these courses, but that doesn’t help a 6th grader.
Also, while the student is working Sudoko puzzles in class, how are her grades? I’m thinking of a bright student I tried to get moved to a more advanced class, because this student can run circles around the students in the regular class, but I was unable to do so because the “available evidence” (the student’s middle school grades in my subject) did not show sufficient aptitude.