We'd like some sort of program that redirects all reads/writes to port 5938, to port 59000. It has to work in both directions, kind of like a "port tunnel".
Is this possible?
Try TcpTrace. (Download link here.) It's a free Windows tool that lets you intercept and forward a TCP port for diagnostic purposes. Note that this is a GUI tool, not a command-line tool or background service.
I've used TcpTrace before for debugging custom socket-based application protocols. Assuming the connections you want to proxy are simple enough – i.e. the application protocol doesn't encode any new server/port information in the payload (such as an HTTP redirect) – then TcpTrace should accomplish what you are asking, i.e. passing the traffic through from one TCP port to another.