An update on how ridiculous this process is:
Booked a flight with these paper vouchers over the phone after being hot-potato'd between EXP agents (none of whom wanted to deal with these).
Did not need to talk specifically to Business Extra Team, despite putting my BE# on res (or so I hope).
Agent charges the full price of the ticket to your credit card, you give agent voucher information over the phone and send the paper vouchers in, AND THEN a few days before your flight date AA will process the paper vouchers sent in as a credit to the payment method (as they said they do it in priority of upcoming flight dates, and Dec/Jan is a busy time).
That is, if you book months in advance you will have to wait months to know if your vouchers were even correctly accepted for a credit to your payment method.
Horrible, horrible process.