I don't know much about rotating bins. If your rotating bin and the other bin are too dry, you need to add more green material such as lawn clippings (I realize you may not have these) and kitchen scraps (no meat, dairy, salty or fatty foods), but such things as melon rinds and vegetable peelings add a lot of moisture. My problem with adding this is that rats break into my bin, so I now just use garden and lawn clippings.

I have an open bottom bin probably like yours, here in So. Calif--not as hot as AZ but hot and dry over the summer. I harvested some mulch out of the bottom today. It was moist, but the top of the bin was dry, so I got the hose and added water. I don't know why your bins seem hydrophobic. I wonder if your bins are in the shade or sun; maybe shade would keep it from drying out. Also, I know parts of AZ have mid-summer monsoons, so if you have that, make sure your bin is open on the top during those events. Collect extra rainwater if you can.

I used to try to turn the material in the bin, but it's too hard so I gave up.

Provided your description is 100% accurate ( just rolls off and seeps out, leaving compost dry), try this. Punch a pin hole in bottom of 1 gallon milk jug,fill with water and sit jug on surface of compost. Us as many jugs as there's room to sit on compost. Repeat until compost is moist.

Report results, that's the ONLY WAY we know if our advice solved problem.

What makes up your compost contributions?

Not having this problem really, except a couple bins are harder to reach for a bit of hose water in high summer dry spells, but klem, I kind of like your idea anyway.

Also I like it for a couple of “ flower’ beds, or a new planting if going OOT , akin to the upside - down 2L soda bottle but maybe simpler. Though, I only have a couple of jugs, intact because I fill them with water & keep in potting shed to water new potting- up things at first. I wound kind to test how long it takes one to empty from a pinhole , though.