Good luck, it is a constant battle for maybe 100 days a year, then we can stop working quite so hard.
I think you are doing everything OK already. I only add that if you can cool off their FEET then they will stop panting.
So watering down their run is good and can you channel some water in maybe @ 5 PM (when it's at it's worst here) so that they can walk around in it?
If I can find it, I'll post a link to a guy in Phoenix AZ who has chickens in a wire enclosure in the summer. He runs water over flat pavers that they stand on and this cools them down. Let me look.
Also, IDK if this applies, but stay away from feeding corn anything right now; it makes them hotter. Even frozen corn treats are a bit risky here during the summer.
And just to make it worse - it's barely June. We still have July, August and September. Yippee.

