You just answered your own question and I'm 110 % sure your gardner snake is eating your eggs. Yes they do eat eggs and once they know where to get them, they will return time and time again...snakes can squeeze through the smallest holes. If you caught a snake in your pen, regardless of what kind it was, they are eating your eggs, not your chickens...they could care less about chickens and wont attack them.... and they could care less if the eggs are store bought or not......I don't kill my snakes because they hunt for mice and the mice like to eat the chicken food and build nests in the straw....Hooray for snakes but a bummer for the eggs........sorry, I hope others will agree.
And-snakes don't return the same time each visit. you may go weeks without seeing one. FYI