We've had the same problem as you, so I intend to rear our next ducklings on 1cm weldmesh held on a wooden frame so the poo just falls through into a shallow tray below (maybe!?). The idea is then that you can take the ducklings out, remove the frame, then empty the tray into the compost heap. I'll start them off with a sheet of old curtain over the mesh until they find their feet, then take it away.
I have no idea if this will work - I just know that what we did before was absolutely not the way to go!! I'd love to know if anybody has tried this before, and if it worked!!