Wow i had the same feeling with my 2 piggies about the poop and the hay. So i went out to buy a litter box and with it care fresh shaving <----- this is what i use before i switched to fleece so basically i put all of their poops in the litter until they got used of doing it in there. Now the great things is not only do they poop in there they also pee!!!! which is the best part cause now they don't pee on the fleece. I spot checked the cage twice a day and only find few poops around it, which is much better than before. The litter box helps a lot cause my 2 piggies don't pee on the fleece which it causes not to stink at all. I change the little box every 3 days, also you can see the pee cause u can see the color of the care fresh darken as they pee on it. If you don't change it every 2 or 3 days it will smell, i learned the hard way
. As far as the Hay all over the fleece i bought a hay rack, but i had a feeling that they did not like it so i bought 2 bowls and put fleece in it and still kept the hay rack so now they have 3 places to have hay from. It keeps pretty much all the hay from the fleece, only a few gets on the fleece cause they go crazy running laps and pushing things around when popcorning.
I hope this helps!