Well this is an eternal dilemma!
Congratulations btw 
what we have is a large run - think the size of a small garage - and it's attached to the chicken shed, with a ladder etc.
It's all covered with galvo roofing sheets so the ground stays very dry, they need dry, it's far better for them to be dusty than damp.
In this sense our arrangement works very well all year round and I never have to remove droppings from the run - they just seem to get turned back into dusty dry earth, they have been in there a year and the ground is just the same as it was.
HOWEVER we have a rat problem (there were rats already, our neighbours have a giant compost heap right over the wall and they came in the shed to eat our trampoline mats 
) and they hae started digging actual tunnels underneath the slabs we have all round the edge, into the run where I scatter the chicken pellets.
I find poison can work but is unpleasant as you find dying rats...not good.
What I should have dine, is lay an area of chicken wire UNDER the earth before I built the run, to stop anything digging its way in.
In your situation, I might suggest that you dig out a little way down, put the slabs back, and then refill the earth on top.
This will stop foxes getting in too. We also dug the surrounding wire into the ground by up to a foot, to try and stop any determined foxes, and slabbed all round the outside for one slab's depth.
No foxes have got in yet, at least! Remember chickies need to have dust baths, so I don't like 'scratch mats' (thick grid wire laid on top of the ground) but if your run is uncovered it may well turn into Glastonbury over the winter