Have you considered adding another stringer or 2 to "frame" the opening. Like putting in a header for a window or door in a building. Maybe a "out of scale" portal? I used a magnetic doggie door for access to my power shed to keep small critters out and that has worked so far. Cats have no issue climbing/jumping my 8' block wall. So far coyotes haven't dropped by but that is probably because of the big dog rather than height of fence.