Sorry, my knowledge is limited too. It does sound like firewall rules on those networks are not allowing the video and audio, so STUN or TURN would help.
There is a nice introduction near the end about ICE (TURN and STUN):
Running your own STUN server sounds doable, but probably more work than you want. TURN sounds like too much work and expensive (sounds like needs hefty infrastructure to relay multimedia content).
Alternatively, there are some public STUN servers you can use. There are some lists that may be helpful:
I may need to try this soon, but I have to deal with other priorities now. Please share if you make any progress!
Cheers,
Paul