Are you aware, that your employees, who might have access to server logs ( if they control the servers with you ), might still see all the connections, which you are planning to forward? Even if you use a proxy or socks ( as well over ssh ), the traffic, the packets and all the connections are logged.
And apart from that, are you really planning to host "hundreds" of illegal downloaded videos on your buisiness servers? You can't seed encrypted files, so all your files have to be untouched, before you seed them to the peers. Your bittorrent-client wouldn't recognize encrypted files, that the peers are asking for, so that you wouldn't be able to seed. If you immediatly auto-encrypt the files on your buisiness servers, after downloading, the forwarded requests won't be found on your servers and would be leeched again and again. And on the other way round, the peers can't find the requested files, because they are encrypted at the time their requests take place - result is: all your files on the buisiness servers have to be untouched.
If you find any solution to hide the logs from your employees, as well as you may hide all the untouched files, they still will recognize a great amount of traffic, which results from your seeds ( let's guess 1-3 tb per month ). How will you explain that to them? Lost in space?
My advice is:
Install a webgui for your bittorrent - client @ home and access this with a browser from your work pc. Even if your home pc is connected via dynamic IPs, you might access the webgui with a dynamic dns service ( example: dyn.com ) and I'm pretty sure, that your browser cache on your work pc isn't controlled by anyone at your company, or you delete the cache, every time you are closing the browser. You might as well secure this webgui with a ssh-connection.