It is working!
It was not that simple since Ports 80 and 443 were not allowed to go via the Firewall (I am assuming that was because the information in them were not typical HTTP or HTTPS). I then tried Port 21 and it worked perfectly fine since it is open for FTP commands and probably a lot more relaxed in the Firewall inspections.
Thank you very much for the guidance.
I was not aware at all how simple nc could listen to a port, and then pipe data to the proper
My final command, since I am using port 21 for the local input, and 3333 for the mining pool, is:
$ nc -k -l 21 0<backpipe | nc poolipaddress 3333 1>backpipe