Yes, I saw that rubber chippings advert - wasn't sure about that at all, they might eat them was my first thought.
We keep lots of ducks but in a very different situation to your so don't have this problem - however, I use plastic grid mesh for the outside of our goats pen - its the stuff you buy off a role at the garden centre - usually green or black and you can put it around young trees etc - perhaps if you put a length of the smaller gauge type under the chippings (and on top of the mud), it would help - you can then just lift the mat/length each week and your chippings will still be on the top - throw them away and replace with fresh.
We use it to stop our goaties sinking in the mud and getting it stuck in between their toes. Works quite well.