So I revisited my approach (I'm not avoiding work, you're avoiding work), and it's certainly difficult enough to pull off: it took maybe 15 attempts to actually get 3 safe hens. I found that the main ways that I died while getting the strategy to work were starvation (due to not eating an egg while trying to turn it into a helmet or a hen), hen explosion (if the number of hens gets over 4 or 5, good luck preventing the entire board becoming an army of angry hens), or just being pecked to death (death comes for us all).
That being said, once I did get it to go off, the game didn't exactly become boring. It's a very different sort of game, but it's still fun. The challenge shifts from "don't get pecked to death or starve" to "how long do I want to let these eggs gestate to maximize my score and avoid a dangerous hen from spawning." I even had a few close calls where a dangerous hen spawned, I had to kill it, and when I was trying to get a helmet, another dangerous hen spawned! This combined with the fact that the only way to make the score increase at a reasonable pace is to get the eggs dangerously close to hatching means that this always threatened to happen.
Anyway, thanks for making this game! I've really enjoyed playing with it and I look forwards to seeing both what you do with it as well as what you make in the future!