FAM - it happened to me on UA a few weeks ago. I knew this because the agent slipped up and spilled the beans. Of course that was shortly before the flight, and yours isn't until July.

Since 4E shows as available on the seat map, did you try changing your seat to 4E?

After looking at the seat map for your flight and also whats for sale (F6) I agree with the poster above, call AA and have them check. Forget my FAM statement in your case (I left it in for reference). A few months back I could not select seats on an AA flight for weeks on end. The first and second time I called they said it was probably an equipment change. The 3rd time, after not being able to make seat selections for a couple months they checked with operations (or some similar group) and mistakenly the flight had been locked for seat selections. They unlocked it and then I could select my seat.