When raising cornish x, you have selected a bird that does not- by and large- forage.
We are currently raising the cornish X next to the silver cross grey broiler. While we raise thousands of birds a year on pasture, we still move each and every one of them three times a day. I would suggest that there is no use in trying to make them forage, and that they prefer to lay in their own feces... there is no way to fix that. Here are a few ways we have allowed them to lay in their feces less: have a feeder on each side of the pen. Distance between waters & feeders is good. Cover the whole pen so that shade prevails. That is crucial. Our meat birds are always under shade, and it is definitely preferred by the birds. I have to disagree with other comments and say that the space you have is adequate, and not only adequate but space efficient. Give them space, and they will not use it.
I suggest raising the silver cross grey broiler as an alternative. They move a lot, they act like chickens, and they don't take 12 weeks to slaughter... only about 9.