In my area May and June are hot and dry, and July and August are hot and humid. We have huge monsoon-like thunderstorms in the summer. I started using deep litter about a year ago, during the dry time. I had been spraying it lightly with the hose to keep the dust down and provide some moisture for composting. That worked great until the humidity hit.
I didn't stop spraying when monsoon season arrived. It wasn't long before most of my birds were getting bumblefoot-like sores on their feet. That could have had a number of causes, but part of the problem was the way I had been maintaining the deep litter. When the litter suddenly got thoroughly moist it became clear I had not been adding fresh litter fast enough. The dry poop kind of reconstituted. It was smelly and gross. I treated the birds' feet, mucked out about half of the litter, and started over.
I resolved the problem by increasing the amount of fresh litter I was adding, and I stopped spraying the litter with water. The birds' feet healed just fine. The litter still doesn't compost much in the coop and the coop is a bit dusty, but I'm okay with that. The coop/run has a lot of open wire and cross-ventilation. Most of the coop/run dust gets blown out and some of the outside dust gets blown in. My birds live in a desert. Dust is something they have to cope with, like heat. There is no way to keep them in a dust-free environment.
When it is really hot and DRY I will spray the coop/run a little. It helps moderate the temperature in there. But I will stop all spraying once the humidity kicks in. And I will muck out a portion of the deep litter every few months.
In my climate the litter may not compost well in the coop/run, but once I get it into a compost pile where I can add a lot of moisture it is a different story. After last summer's coop muck-out the compost pile got so hot it was scary. For a couple of days I was concerned about spontaneous combustion. Watered and turned it a lot and it eventually calmed down, producing a great compost within a few weeks. I like it to be in the "active" range of the compost thermometer, not off the scale on the "hot" side.
Since I need good compost more than I need eggs, this works for me.