Just remembered to come back and give an update on this
thread. As soon as I stopped giving the
chickens the prickly lettuce weeds, their egg production started to go back up. I am now getting 5-7 eggs a day from 11 hens (not counting one who has been broody).
Meanwhile, the game cam had showed a) only a small number of hens going to the nesting boxes, and b) no sign of predators.
My best guess is that, even if the weeds were not harmful in small quantities, something was building up when they were eating too much. Or the hens were just gorging themselves so much on the weeds that it was unbalancing their diet.