TeamViewer repeater service?

I provide support to a remote factory location.  All factory computers are on a local network where internet access is 100% blocked.  Currently I use TeamViewer to connect to an office PC then I start a VNC connection to access the target machine on the factory floor.  While this is a workable solution, the connection is very slow at times.

Is there a way to make the middle computer some sort of repeater or passthrough so that TeamViewer can make the connection directly?  I understand that the answer may depend on exactly how IT at the remote site has configured things but I am open to suggestions.  I could probably get IT to set something up but I have no idea what to ask for.