Agree with Karminski about the slabs, loose laying them with spaces between will also help drainage as you'll want to hose them down sometimes and also it will get wet with rain. You'll then need to cover the slabs with something like hardwood chippings so the hens have something a bit nicer and softer for their feet, and to dig in, then you can pick up the pooey bits each day and keep it clean. Personally, instead of slabs, I would cover the run area with strong landscape fabric, fixing the edges down underneath and outside of thre run sides. This provides drainage and also will stop the birds scratching in the earth and making everything muddy and you can then lay woodchip, or like me, rubber chippings on top. The mess will still come from above in the form of poo, but not also from below in the form of mud.
Any chance of extending the end of the run to give more space? I agree with Chris about only two hybrids and avoiding breeds that don't tolerate confinement very well, but if you went for small bantams 3 would be OK. How big is the coop they roost in? How long and how many are the perches? that will affect the number you can keep comfortably, even if at some point you could consider a run extension.
Everything will stay much more comfortable, drier and cleaner if you cover the top of the wire on the run with something like white or clear plastic tarpaulin, which is cheap, easy to fix, lets light through but gives filtered shade. If you take it down the side which is facing the prevailing rain and wind the birds will greatly appreciate this shelter as well, as chickens need shade and hate wind. I got mine from Tarpaulins Direct at http://www.tarpaulinsdirect.co.uk/TarpaulinsSite/product/MN.htm and they're still going strong after nearly 3 years round the end and sides of my run. Yuo could even fix the tarp over the top of the coop, if you could do this without blocking any ventilation, as it would help to keep it dry. Don't worry about sealing the joins hermetically against draughts, chickens need lots and lots of ventilation, but you do need to make sure it's waterproof of course.