I don't have the same model you have, but there are some things you can check.
Pull the registers off and make sure the runs are sealed and not leaking. Especially the ones on each end.
If they are it's just blowing the air into the attic. If the ends are open, seal it with expanding foam or something similar. If the others are not sealed, use furnace tape on the connection.
You are correct, AZ. gets hot. If you don't have a 15000 AC unit, and don't want to put an additional one over the bedroom, then changing out the 13500 to a 15000 is another option.
Good luck and welcome to the forum.