<de-lurks>
Hello,
Just thought you might be interested in a solution I came up with in a similar situation (device connected to a 4G router, and therefore using CGN, which we needed to be able to establish external connections to);
The 4G router we are using has a VPN client so I created a virtual private server (VPS) on Digital Ocean (the cheapest machine available is $5 p/m and includes up to 1TB of traffic, plenty I should think). We establish a VPN from the router to the VPS and, with some port forwarding set up in iptables, we're able to talk to the device connected to the router at the other end of the VPN using the VPS's public IP address.
If you can create an outgoing VPN from your router you might be able to do something simliar. However, in terms of gaming this might add a bit of latency to your connection - it's not a concern in our use case so I haven't tested it.
Edited by deleted (Mon 07-Sep-15 16:52:10)