My 6th grader matriculated 8th grade math from his private middle school. the local public high school refuses to help with continuation of advanced m

The school has the right to teach its own program.  The terms "8th grade math" do not describe the level of math, only the grade in which your son learned the math.  It is possible that the school is giving him the next level of math without calling it "9th grade math".  You need to look at the topics being taught.  Is it algebra?  Geometry? Pre-calculau?  Don't get fixated on the grade level.  Different schools introduce these subjects at diffferent times.  If he has already completed geometry, and they are trying to teach him geometry, ask for him to be tested on that subject, and upon successful completion on that subject, move to the next level.