Just an update for anyone that might be interested:
I put 1" chicken wire on the bottom of the ark a few days ago, and so far it seems to be doing what I intended it to do. The chickens don't scratch the ground bare anymore, although they aren't very good at eating the grass evenly! haha. They have a tendency to eat the grass very short in some places and hardly at all in others. So, my lawn will never look great. (not that it ever did before... we've never been very good at yardwork around here.)
Despite the grass looking uneven, I am really liking the fact that cleaning up the poop is so easy now! Every time I move the ark, I use a small rake to collect as much of the droppings as I can and throw them in the compost bin. Then I just use the sprayer on the hose to water in any remaining poop into the grass. So much better than having a dusty, dirty run with poops that are difficult to clean up completely! Not to mention the icky mud in the wet winter-time.
I do wish my yard was a little larger so I could have more options for ark placement. We have 3 small kids and a swing set, so I do have to leave some space for that, lol.