Jusst fyi, this spring the run was so muddy that I put down 4 bales of straw. It seemed to work great, but then 2 hens died... enter sour crop and impacted crop. They were ingesting the straw and it was coiling in their crops and clogging up the works. I raked out the straw as fast as I could! Going to try other organic stuff now.I had sandy dirt(well, still do under the semi-DL)...it was very, very stinky when wet,
both after a rain and even worse during spring snow melt.
Molds are everywhere and the changing environment of a deep litter could cause you problems if a mold bloom happened, it would normally even out if you had the right mix of ingredients, but you might not want to risk that. I don't 'see' mold, but that means nothing for your sensitivity.
I found early on that even tossing down a thin layer of straw can greatly help with the odors, but some mold could happen then too. No one can predict what would work for you in your environment.....a mask might be necessary when working in your run.