Southern AZ is at 92 F today. Last I heard we are supposed to reach 100 by the end of the week.

We have a dry heat but usually reach around 115 F at the peak of the summer.
Here's what I do to keep them cool:
1. Hang shade cloth on the side of the coop that faces the sun. My coop is almost all hardware cloth, except for their roosting area (surrounded by plywood) and roof (corrugated sheet metal).
2. Put out bins of water for them to sit in (they also drink out of them, so I refresh the water once a day).
3. Freeze fruit for them (they especially love watermelon).
4. Make sure their waterers stay in the shade and don't overheat. Sometimes on really hot days I even freeze some yogurt containers of ice for their water.
5. Hang fans to get some airflow in the coop. Chances are they'll get pretty gross, so I like to have fans that are just for the chickens.
6. When it gets over 105 F, I like to spray down them and the coop in the afternoon. I don't like to do it too much because wet, hot climates are perfect breeding grounds for bacteria and illness, but I figure it's okay since I live in a pretty dry climate.
7. Keep electrolytes on hand and do some quick research on how to spot heat stroke/exhaustion in chickens.
Good luck keeping your birds cool! So far it sounds like you're on the right path. I would make sure to always let them out into the run/yard early in the morning, as they will need a little more ventilation to combat the heat than your coop provides.