Last year they changed how they assessed kids during the first half of the school year, so you maybe in better shape than you thought. If you get the application in before December he will be assessed as if he is a 6th grader so maybe you could use the Explore test. It maybe worth it to ask.
We did not use either test for DD10's application because we had an IQ and achievement test score. Would it be possible to get those results instead? There maybe someone at his school that is able to administer them. Or, if there is a university around with a college of education, you could check there to see if someone there would give those tests.
We did have DD take the Explore test as a just in case, but as it turns out she didn't do well on the math section (she gets too anxious during times math tests) as Davidson requires.
We are not there yet, but are in the process of moving there as I write.