Where I live, in TN (and before I moved here from VA) Brown Recluse spiders were super aggressive. On the occasion where I would find them skittering across the floor or deck, they would jump at me. I even had one chase me across the living room before I managed to squish it with a shoe. Anyway, they certainly need to be taken care of. Could you dust under the coop heavily with DE? I'm not sure how effective it would be, but they are small spiders and I'd think it would cut their exoskeletons and dry them out like most other pests? If not, flipping the coop over and squishing them might be a good idea!
Good luck!