Pea gravel is to ducks what sand is to chickens. Get some pea gravel!
I was so sick and tired of the mud pit and filthy ducks and the smell. The gross baby pool, the yucky waterer. Icky ducks! 2 tons of pea gravel covered their 10x10 run 4-5 inches deep. Was $100 delivered. WAY cheaper if you can pick it up yourself. Same price about as buying it in bags from Lowes or somewhere. I placed a non-biodegradable flower bed liner on the bottom, something you won't have to do on concrete. You would only need a skirt of treated all weather wood around to hold the gravel in.
Let them poop on it all day, hose it off in the evening. Fresh and new for the next day. NO MUD! No poo slicks since it sinks into the gravel a bit, specially when they walk on it.
Anything organic will smell when it gets wet. That goes for mulch, shavings, all of it. Poo + Water + Organics or dirt = stink and grossness.
You're half way to easy management with the concrete pad.
The rubber mats can grow mold under them so you need to lift them and clean under them periodically. You can hose them off same as the concrete. But it will still create the "poo slick" since it's a solid surface. Better on the feet though. But the gravel... helps out a lot.
Where I have their outside food gets crud on it. I can take a kitchen strainer and do that corner and wash out the food debris from the gravel as needed. Keeps bugs down. Doesn't take long at all.
Too bad they poop in their pool, I bought them a smaller infant sized one so that I don't feel so bad dumping it daily. The big 6ft pool was just too much water.
At least you're not dealing with mud, that's the worse.