As expected, only the more expensive awards are available. They'll sell you tickets for lots of miles but not, at the moment, for few miles or economy + miles.

JDiver's explanation of inventory allocation is (unsurprisingly) much clearer than my sketchy attempt above and, as he points out, mid-May sees the peak season starting. Semesters end, more people travel (typically, May 15 onwards means higher fares). You either need to take a chance, and quite possibly not get upgraded, or be more flexible. Alternatively, you could cough up cash or use the miles for that AAnytime award.