I would second the suggestion to go get copies of prior years tests. I would go so far as to create a practice test, as an exact duplicate of a prior years fall 6th grade test. Administer and grade that yourself, and see how he does, and if there any shortcomings, you can see exactly where, and work with him in the evenings to master those concepts and computations.
I am not too familiar with computerized adaptive tests. The idea of being immediately graded on each question, and the balance of the exam then being adjusted to that answer, spooks me. It removes the "second look" opportunity, which is not only valuable for correcting errors, it's an extremely important habit to form, IMO. It also sounds like it could lock you into a lower score based on a single error.
As far as his placement next year, I would take it upon myself to work with him in the evenings, to try and bring the standardized score up in spring. If you feel certain he is ready for the higher level math class next year, I would absolutely advocate with the math teacher and principal to ensure he gets placed appropriately.