The boards above the shavings are the roosts?
if so I think they are to low. You may need to get creative in how to raise them.
if it were me I would see if there was a way to put them going across the other way a nd not just in front of the nest boxes.
them all using one box is certainly not unusual. I have over 20 birds in my main coop and only see eggs in 3 or 4 of the nest boxes.
As to getting their bums cleaned up.....can you get some dusting box things like fine sand peat moss, wood ash (no bbq ash as there are chemicals) and or dry top soil? If so I would make them a 2' x 2' box 10" or deeper to dust bathe in. You would need to put a roof over it to keep it dry. If their bottoms are super dirty you may need to give them a soak in plain water on a really warm nice day.