I think what I would do after HSing is have the school administer the end of year test for the age-grade child would be going into. Then have the next grade level test administered if the first test was high enough - get an agreement on what the cut=off is beforehand.
What someone told me she did for her son, since nothing was going to happen at K-5, that when it was time to move to the middle school for 6th grade, at the end of 5th grade, she had the district administer the end of year 6th grade test which he aced. So he was accelerated to 7th grade upon entering Middle School.
