Fraser, I play mostly CoD and that is my primary focus, so as far as it goes that is where I have seen this issue. Now that I am back I can talk about some of the items above.
I have a BGW210 gateway made by ARRIS. I tried changing the NAT from "Secured" to "Open" as you suggested, it did not change the double NAT when I ran tracert 220.127.116.11, the exact same private IP address showed up.
I did a bit more researching and it looks like I'll have to talk to tech support with AT&T. I found out that NVG and ARRIS gateways can actually be used in bridge mode, but I have not tried it yet and will likely get with AT&T to have this handled.
Link to AT&T forum with instructions on IP Passthrough and DMZ setup on AT&T gateways (They say it's IP Passthrough, but the links in the "Solved" post for NVG/ARRIS take you to bridge mode setup for an NVG gateway): https://forums.att.com/t5/AT-T-Internet-Features/How-To-Setup-DMZ-and-IP-Passthrough/m-p/4320234#M3837
The link for NVG/ARRIS redirects to this page: https://forums.att.com/t5/AT-T-Internet-Features/How-to-put-the-Motorola-NVG589-in-bridge-mode-or-as-close-as-you/td-p/3552057/page/2
The second link I have posted shares a lot of info on my BGW210's setup that I didn't know about, not sure if this will work but I'll give it a shot and reach out if its better.