I'd agree that 6 months is normally enough time, given that is what most other candidates will have these teachers for.
It sounds like another junior year math teacher might be available, as well?
If you cannot get an alternate and this teacher insists on more time, your son should call your BGO. Sometimes we can work with school officials to give them the run down of the teacher recommendation and calm some nerves down. USNA really doesn't want a recommendation with a handful of "not observed" blocks -- otherwise it serves no purpose. They would rather have you wait until the teacher feels comfortable.
Now I am not intimately familiar with the recommendation form, but I believe it asks for comments within the classroom. WP provides some great ideas of prepping the teacher for what USNA looks for (in case they have no idea about service academies). But the scope of their expertise should deal in the classroom, study skills, time management, classroom leadership, etc. Not about how Joe is a great football player -- Admissions will already know that.
Not that you have any control over this, but longer teacher recommendation write-ups/free comments, does not necessarily equate to more effective. Examiners review a plethora of these applications for every board meeting and assuming USNA hasn't character limited the field, a lengthy write up could lose the examiners attention quickly. Additionally, each candidate has at most 1-2 minutes in front of the Admissions Board. A concise, to-the-point write up with 1-2 examples is probably enough.