Any other ideas besides pellet guns? Neighbors yard with young children close. I have a doggy door with heavy rubber flaps. (Can seal closed at night.) If I lock out the blue jay, I am also locking out the hens.
If you use black landscape fabric to create a curtain in a way the hens have to go through the curtain to get into the nesting area that will stop corvus species getting in "they can't afford to go into a place if they can't see what is coming in their back, but you have to eliminate the ones who tasted the eggs, those ones will go in regardless, but even if they do, if they can't see their back it could be a death trap for them as they can't see you coming to get them "that depends on the design of your coop".
I hang bird feeders all winter with wild bird seed and suit feeders, and I put out humming bird feeders in the summer and take up the wild bird food. Always have. I have never had an issue with dependence on my food supply. An occasional bear will treat himself to the suit, but up here in the mountains, that's just part of living here.