I've NEVAH cleaned a run. Some folks take a tiller to them if they get compacted. Mine is a bit compacted around the new coop. That's because the new coop was built on heavy clay subsoil that never got raked/de-rocked enough, or had enough time last fall to get seeded to grass (We didn't get the coop finished until late November). So 1/2 of the run is nasty clay subsoil, that is getting reconditioned by adding all the compostables I can get my hands on. (the other half is weed/grass quite lush and healthy looking) We have a bagger on the lawn tractor, and that stuff is gold IMO. It goes where ever most needed. (on potatoes, in green house, in chicken run or chicken coop.)
If your litter is composted in the coop, be sure to leave a good base. Are your coops bare ground? Bee Kissed uses DL in bare ground coop, and NEVER takes any litter out unless she is harvesting it for the garden. She never has flies or odor in the coop. But, she free ranges exclusively, so doesn't have bare ground run issues to fix.
Yes. That stuff would be gold in the run. PDZ is Zeolite. It binds nitrogen (thus no ammonia smell in the coop) and slowly releases it. I've never used it, but IMO, think it would be fun to try in a heavy nitrogen based compost situation. The more organics you can get in your run, the healthier your run will be (unless you already have a healthy crop of grass/weeds). I'd be happy to have a 6" layer. If I had a 6" base in my run, the next thing I'd do would be to collect an army of earth worms and introduce them at night or in rainy weather. (so they can get some good soil penetration before the chickens find them in the morning.)

I got it... Reminds me of the dyslexic agnostic. He never did figure out if there really was a Dog.
Yep. Get that bare gound covered!!!
If you're doing BCM, why are you doing CM? My understanding is that the CM don't have any near the dark egg color that the BCM do. If you're incubating your own eggs, you have nothing to loose but time by experimenting with your humidity. Now, if your chicks are dying during lock down, I'm wondering if the egg is too wet... or the chicks are too big and malpositioned (good enough reason for an eggtopsy right there). My first hatch this spring had quite a few DIS. (final hatch was 19/28 I think.) I did open up a few and decided that they were either too wet or possibly malpositioned. I didn't do a complete eggtopsy on all of them, b/c I didn't want to look at all that death. BUT, with the next hatch, I left them on their sides UNTIL lock down. Then, because I didn't like the size of the air cells, I put them in egg cartons for the hatch. That ended up being the best hatch ever!
Just for grins and giggles, and to humor me, try putting your next hatch in egg cartons (if that's even possible with your Brinsea.