If you know you are going to be using AE to book STAR awards, does it not make sense to transfer you MRs ahead of time so you don't run into this problem? Since it appears you do this often, this seems like a logical way of ensuring you have the AE miles when you try to make the booking. It is clear you are not using them for anything else (merchandise, reatil cards, etc.) so why not just move them into your AE account every so often?

BTW the Amex Program is called Membership Rewards, and these are points not miles...