right now the door slides in a channel... (highlighted in green) instead of it completely riding the bottom of the channel, it would be partially supported by the ORANGE (circle) wheel that is attached to the motor... if necessary the door could be supported on two wheels, one being driven, one free wheeling(just for support)
It's cheap enough to try it... I've only made vertical doors so no experience with a horizontal door. It does look like you need a longer track on top and bottom so the door is fully supported when open and less likely to bind in the open position.
Next part would be which RPi, the Pi zero ($14.00) is great, but not POE without adding an ethernet HAT/Splitter($8.00),($10.00) one micro USB, speaker Bonnet with speakers ($15.00)...etc I like it because of the size BUT it ends up being more expensive than a Pi 3 B+
($35)... which has POE via splitter($10.00), 4 × USB 2.0 ports . Having that many USB ports I can run 2 USB cameras,( as well as the Pi ribbon camera) and USB speakers.
A Pi 3 case with a fan is $10.00...
I guess that is sorta like an encoder but with only one channel (encoders usually have 3 channels typically A, B, Index)
It would be way simpler to use the slot photo sensor as limit switches in your code. If I used that kind of sensor I would make sure the target that is used can't come into contact with the sensor. So typically the sensor is placed to "see" something that passes by and if an over shoot happens the sensor is not in danger of getting damaged. With chickens comes dust so any optical sensor is subject to failing if not kept a bit clean. That is the reason I use those magnet switches typically used for home alarms.
You might look into some kind of smooth operating drawer slides for your door...
I've never needed a fan on a Rpi 3B, just make sure you have the heat sinks installed.
Is a cheapo solar panel enough to run the Raspi 24/7 ? I am thinking about using an arduino to try and save some power draw as I'm not in a very solar friendly place. I was going to power it up in a nearby shed and then use IR to send commands across a gap. Using solar panels just to power the lights. I didn't want to run the controller off of the solar.