I found that I don't care to eat anything I have raised - I certainly could if I was hungry and had to have food, but that is not the case. I just loose my appetite when they are cooked up.
You don't want to add moisture inside coop, it will encourage mold in the humid weather. Grass clippings if fresh could maybe be put in the run, but when allowed to sit for even a day or so, are very musty and should not be used in either the pen or run.
Try training your birds to come when you shake a can of scratch grain. Never feed them any except in the run, and not until you have shaken the can and they come up to you. My hens come running from all over the yard when they hear that can shake, and me holler "Chick-Chick-Chikee!"
Your run is big enough for 13, how about the coop?
Dreamz, You will find that as your birds get older they will start eating a wider variety of things, just like human kids. Just keep offering them different stuff.