Just to be clear; the chooks will scrabble down to the bare boards no matter the depth of soil or litter? I've noticed some [not all] of mine do this in the nesting boxes no matter how much mulch I put in there. They'll even toss the excess out.
Optimally, given I'm only semi rural so have some serious restrictions to consider, would you let a broody have her own enclosed coop & run & let her choose her nesting site, or provide one you want her to use, just more suited to her nature.
If I ever get this extra land my soul covets I will be planning for this & would prefer something the chooks are happiest with.