Another thing I didn’t think of. We are going to put the hinges on the outside. It’s the simplest solution. And, apparently the obvious onePics of the door.
You want that opening OUT. If there is heavy snow you need to be able to clear it. If it is in the run that door won't open. Not to mention if you leave it opening inward guaranteed a sick hen will lay EXACTLY where she would get crushed, mangled, run over by opening a door inward.

I’ll take one tomorrow. You can see it in my other pic, but without the wire it’s not easy to really see it.