My stupid cat has on multiple occasions locked herself in my bathroom by getting behind the door then flopping down, which pushed the door closed. The solution I found was “door pinch guards”. Little foam things that go on the door to stop it from fully closing. Originally designed to stop toddlers from pinching their fingers in the door frame, it works great to prevent my cat from locking the door on herself. That plus your rope strategy may let you keep the door kind of but not fully open. Something like this

A novel approach to SCP-871 containment