a few ideas that came to me today, i'll just put them here for record
actuator may work on 9 volt battery.
use the same method to open but use a small weight dropping to lift the door, perhaps the actuator punches the locking device out of the way or there is a cable of some sort attached to the actuator that pulls the latch out of the way
use original actuator method to close door, but use a heavy door that will overcome a damper (screen door or cabinet)
use a swinging door and have the actuator just punch it shut and pull it open (with no thought to the locking mechanism)
use swinging door where actuator either:
pulls out of a weight hung by strings and pulleys and closes the door, latch is similar to OP's latch or maybe just a baby proof cabinet door latch
pulls a pin out of whatever holds the door open and door closes via spring, bungee, screen door spring/damper, leaning 2x4 or whatever can be used to close door.
ok and here's the fun one!
use sprinkler timer to fill bucket as posted elsewhere
BUT when the bucket hits end of line, have it tip and spill water into a chicken waterer. assuming that either a small bit of water will close the door or that you have a lot of thirsty chickens.