I'm going to throw this out and see what everyone thinks.
If cat5e is adequate, they make an outdoor aerial version (air core so no messy gel to deal with) with a steel messenger cable. You could terminate a piece of this with jacks at either end and form a loop in the messenger for hanging from a hook. Use a 1' patch cord to connect to the jack on the ceiling and whatever length patch cord that is required on the other end. Run the lower end into an 1110 type box and anchor the messenger to the ground screw. A receptacle style jack mounting frame and flush metal cover will finish it off cleanly.

Someone might have to advise on the use of outdoor cable indoors since it will not be riser rated cable. I think a case could be made that it would be acceptable as long as it wasn't permanently attached to structure or passing through walls.