For me, I always make copies of the vouchers and send to them via some sort of online trackable means (signature confirmed, certified) so you have proof of mailing.

Next, AA asks you to list your last name and date of flight and flight number on the envelope under return address. AA processes the mail-in requests by how soon the initial flight is going and depending on load of requests. So, if your flights are within 3 weeks, they would prioritize yours before someone traveling in several months.

Your flight reservations will show as "Purchased" on AA.com as they must receive within 2 weeks and will not turn to "Ticketed" until they have processed the vouchers. If you have send with 21 days notice, you should be okay.

Last year, I sent in vouchers in mid-Jan for a trip in May and they processed them within a few weeks after receipt. I'm sure yours will be processed soon.

Hope that helps.