Here is the shimano nexus trike.
Torker Tri Star 3 Speed Coaster Brake Hub
here is the s3x in a wheel set. I'd look for the hub alone. and use it as a jackshaft as I do with the trike tranny, by attaching a sprocket.
The 'lash' they speak of is the amount of play between backwards and forwards drive. It will drive backwards at all three speeds.