I think a huge factor to be considered about wood chips is your climate. In a climate that sees a low relative humidity between rainfall, the chips can dry out and mold will not be able to set in. In a more warm, humid climate - such as what we see around here (NE Kansas), mold is a certainty. We keep wood mulch in our flower beds out front, and it's only 2-3" deep. Guaranteed every year when I rake it up to replace it, down about 1.5" we'll have white mold. I can't imagine the moldy mess I'd have if I kept 8-10" of wood chips anywhere around here.
Personally, I'd never use deep litter wood chips in the run for that very reason - especially not a covered run that gets minimal sunlight to contribute to drying. But, if it works for somebody else, I won't argue with them.
In my climate, I'd use coarse construction sand. It won't dry all the way through, but it also won't mold.
Is that white mold you see identified as Aspergillus fungus, or another type considered harmful?