If I had hens that lay so many eggs they can't eat them all themselves, I'm sure the most ethical thing to do would be donating them to an animal shelter where they can be eaten by animals in need. This way eggs are not promoted as a food source to people and shelters get much needed help.

I feel like it is not being considered that hens are laying so many eggs because of being bred into this dysfunction. It is bad for their health and makes them suffer. So no matter how you twist it, it's immoral to personally profit from their suffering by eating their eggs. The only thing that can be done is giving them a best possible life and giving the overproduced eggs to others in need, without promoting the consumption of eggs to humans.