You have several options:
1. Call AA and just pay the very minimal phone ticketing fee to get Business class awards for the Business class AA miles. No one should submit to paying Business award miles to fly in economy-that is fraud.
2. Use a service to do the work for you(there are a LOT of websites on Flyertalk that do this). You will pay anywhere from $150-$350 for two people but depending on who you use it can be money well spent. I have a service I found on FT and they have been great at booking me in the class I requested AND follow my flights(and family members itineraries) if there are delays on the flights. Money well spent for me at least. I will be a loyal client for many years.