I had this problem and put golf balls in the nests: problem solved. I can imagine that a few pecks at a golf ball is a powerful disincentive for egg eating.
We also feed them kitchen scraps. I read somewhere that they can get bored, leading to eating their eggs.
This strikes me as odd: fascinating as they are, they only slightly smarter than the average maple leaf; but I have to entertain them?
No problem. First thing in the morning I'm out there with my guitar and we have a sing-along. Then it's book club time, followed by ping pong (those three toes are surprisingly good at gripping a ping pong paddle).
At nap time, I read to them from the Iliad -- or, sometimes, if they're tired, The Incredible Journey, and after some charades I'm off to work. Usually late, of course, but it's worth it.
But really, the golf ball thing did work.