Wouldn't your AAM have an account you can define to as "From" when sending to Exchange and you can add that to the list of accepted senders?
Are you stuck because you think AAM can only send as 'anonymous' and you've got to open the flood gates to that DL to let AAM pass messages?
Haven't looked explicitly, but I've done some AAM with full blown Exchange integration in the backend, and there is certainly an account it uses to do all that stuff, so I would expect that functionality to be there for you at the lesser level of just "forward vm to email