Well, I would empty out their coop and make sure their are no animals in there that shouldn't be in there. Look for any holes or anything that might need sealing up and then when you herd them in at night you can lock them in and they will be safe and probably feel safe. I don't use a light, I honestly swear by natural light by extra windows or the roofing I suggested yesterday. But yes maybe cut the grass and remove anything preventing them from going inside. I didn't catch what area you live in or climate but if after ruling out mites, diet, age, sickness, or state of the coop, is it possible you have something sneaking in and eating egg?in the summer we get a lot of snakes and other things that would eat eggs so I check my coop periodically and at dusk I check on everyone before locking them in. I lock mine up at dusk until dawn for their own safety, we have a lot of coyotes, wolves, the odd black bear, and a cougar in the area.
Chickens tend to be happiest when you let them do what they want, some breeds like to ground nest as well. Is it possible you have a breed that prefers to nest outside?