I'm nearly 100% that the shoes are on correctly? (I have a small trailer manual, but it only shows one side). During the hub adjusting, I did notice that one side tended to bite more when rotating the wheel backwards?, however I did exactly what you said, adjusted shoes at hub, then cables, then long threaded rod up to hitch.
The thing is, it will reverse fine (doesn't lock up) once the hitch is not in the compressed position, which make me think its a problem at the hitch end?.......If there was rust on the hitch slider internal (preventing it from self extending once on the move) could this cause the problem?