Well, I don't have shade, short of digging up a 50 foot shade tree, they will have to wait til my baby trees get bigger.
And as I stated before, I literately have no shade til about 4-430.
So make your own shade.
Stand a folding table next to the run so it casts shade inside the run.
Get a big patio umbrella and put it over the run.
Get one of those top-only tents that people use for outdoor parties, and put it over the run. Or a portable "carport" (tall poles with a tarp-like top.)
Use a car or your house: attach tarp or shade cloth up high, attach the other end to the ground, and it makes a big diagonal shady spot. Put the chicken pen underneath.
Put posts in the ground and attach shade cloth or a tarp to them, so it's above the chicken pen.
Get more PVC and make a great BIG arch, cover it with shade cloth or tarp, put the current pen underneath.
Use tarp, shade cloth, bedsheet, piece of plywood, umbrella, wire mesh with tree branches or hay piled on top, a wood fence panel...
(etc, etc)
One reason trees work so well is that they have LAYERS of shade. A single leaf (tarp, shade cloth) blocks the sun's light, but the leaf itself gets hot. If you have one layer of tarp, then another a few feet lower, and maybe another lower yet-- it makes quite a difference in how cool it is at the bottom.
To deal with the sun moving, make the shade LARGER than the pen. That way the sun can move and the chickens still be in shade. (Covering the sides of the pen would block both sun and air--but you don't want to block air, so don't cover the sides of the pen.)
If you can get some shade set up, the chickens stay cool better without you having to run in and out doings things all day. And they are OK even if you have to be away for a few hours. (If you're buying groceries or going to the dentist, you aren't home to replace frozen things.) Of course you can continue with cold treats too, but you've already said you're short of freezer space. And if you can only do one thing, shade is even better than cold food/drinks.