Can you use your son's resistance to medication as a way to help him become more efficient? For example, you can point out two or three specific behaviors that the medication is supposed to help with (such as the ability to be more organized, or the ability to focus and sustain attention better, etc.). Then you can suggest that it is these very areas that he's having difficulty in. If he disputes or denies this (which would be pretty common for a boy his age), then you can ask the school to give you very objective behavioral evidence of these difficulties (checklists, teacher observations, missed assignments, deadlines, etc.). Then, you and the teachers (in as non-threatening a manner as you can) can present these "facts" to your son. You can ask him to come up with his personal goals for improving in these areas on his own (or with any help he needs from adults). If he balks at this, you can ask him if he thinks he's doing acceptable work. If he says yes and you or his teachers know that he is capable of doing better work, then you set the goals (and the rewards). If all of this fails, then it's a good time to re-examine the medication issue. You can then say: "Son (or whatever it is you call him), you tried it your way, and we're proud of you for that, but it isn't working. It's time we thought about that medicine again." And then I would take him to his pediatrician (who should know all about this in advance), to make the case for meds. It may help your son to think about it this way: "If you had diabetes and we knew you would lead a better, longer life with insulin treatment, we would make sure you had it. It's kind of that way with Ritalin®."
There's another important point here, and that's the trombone. The threat of losing music just might put your son into another gear, but I would be very cautious about taking away the one thing he is doing well. Sounds like a key player here is the music teacher. Make sure he or she is part of the team.
I always try to find the area in which a child is doing the best and try to replicate the features associated with success into other areas. What is it about the trombone or music that allow him to override some of the negative effects of the ADHD? Try to build these into his everyday schoolwork. In music, does he feel competent? Does he feel that way about his schoolwork? Which subjects? Build on those strengths first. In music, is he motivated? In which academic subjects can you say that? His teachers can build his motivation by reinforcing and encouraging his academic strengths, rather than by focusing on what he can't do well.