I'm another one who uses AA miles for coach to Europe. I have used them for J but for me and my husband, a short trip to Europe (under 12 hours) isn't that bad in economy. (My husband is 6'3" but luckily we almost always get bulkhead). We haven't had any trouble getting MilesSaver economy awards to/from Europe this summer. We got J to South Africa (on Iberia metal) last September/October but we booked it pretty far out.
I agree with others to call AA for some other options such as Iberia that might not always show up. They always waive the booking fee for us.