Great news, Red! So glad you got a chance to see the doc. Now, why would you go through all of that, including getting that nice lady from your school to call in favors for you, and then disregard his advice?
What I'd like to see you do is tell the coach the situation, ask him if you can try out without throwing so he can see your glove, speed, athleticism, great attitude, and hitting (if possible) , and see if that's enough to get a provisional spot on the team. It seems it would be more likely if he has seen you throw before, but if you're really athletic, and you show great attitude and work ethic, he might make an exception.
Most coaches I have had and have worked with will not grant a player an opportunity that other kids have not had, i.e., a tryout after the roster is set. Your coach may be different, so ask him. Either way, disregarding your doctor's advice is probably not the way to go.