In answer to you question about how to present yourself, you should be totally honest. If you are the section leader, say so. In my opinion, it is bad practice to take advantage of someone's generosity by manipulating them into thinking what you think may produce more results.
If you are going to call, ask for someone in public relations, or promotional departments. You will need to speak to a manager, so be prepared to give the basic story at least twice.
If you are going to write a letter, make sure it is very well written and professional. Just because you are a high school student doesn't mean you need to write a formal letter like you would text your friends (not accusing, just warning). Spelling and grammar are important, so check it multiple times, have your parents check it, maybe even ask your English teacher.?
Regardless of your contact method, don't beg. You need to convey a genuine sense of need, but maintain pride and dignity. Begging is unlikely to produce results. People feel awkward when they are on the listening end of that.
Another thought, if one of your parents is the booster President, you may even consider having him/her draft the letter. Even if you are student leadership, you are a student; a staff member or booster leader will be much more likely to have success.
I wish you luck in getting heads.
Assuming you are successful, I would recommend using a relatively low tension on your high drums. The higher the pitch of a head, the shorter its life. If you tune low, you can raise the heads (very) slowly, and you will be able to get a longer life out of them.
Happy Drumming!