The door catch idea I had was rendered unnecessary, as so many inventions are, by poking around in Home Labyrinth for a while. I eventually settled on a wooden dowel and some broom clips. Now you slide the bottom of the door into place and press the top. It’s easy enough to pull off when you need to, but firm enough that I don’t fear losing the door going over bumps.
Oberian dairy goats in Oregon's Coast Range Mountains