Oh dear, SO sorry to read this! There is another culling method, using ether in an enclosed container. I don't have a link, but I expect you can use the search function above to find it. To me, it seemed the easiest. I think I could kill a meat bird using a kill cone, but perhaps not an injured beloved chicken. I'm sure you'll choose the method that feels right for you.
And again, so sorry you are going through this! <hugs>
Thank you so much, everyone! A neighbor sent over her husband who took care of the job for us. We now have our 3 dead hens in a cooler under our big pine tree, waiting for Saturday when we can get a hole dug.