I have the Omlet/Eglu auto door and it is side to side. I love it - you can set it for a specific time or on a light sensor. It hasn’t failed once in 9 months and I’ve only changed the batteries one time.I would be lost without my auto doors. I have one coop where the door sensor is under a ton of trees & then the coop roof & it's very dark - it still works just fine, no one gets locked out (or in). The sensor is very adjustable, but it also has just a plain old timer.
I think it's eglu that makes a door that slides sideways instead of up & down, maybe that would work for your set up without much modification.
I have not once had a door not shut or jam up because of debris in the track & I don't clean them out.
I have 2 Chickenguard doors & would buy them again if I ever needed - they work perfect in my situation. But there are quite a few others out there, probably cheaper ones too.