Some people have stuck (wedged) a piece of cardboard or a box big enough at the top of stacked gates to have more height, that sounds kind of awkward (I've always had multiple gates to stack to start with having had dogs so I haven't done it,) but if it's doable, might be an option, to McGyver something more at the top. Then however you'd wind up putting it up and down to go through.
Don't know. A thought.
Don't know. A thought.