For me getting moderate NAT is as simple as disabling UPnP and any Port Forwarding rules. If your console is online and connected at the time you will likely need to reboot it or refresh the network connection somehow as in my experience it doesn't seem that disabling UPnP from the console kills the active connections. Of course you will need to also close the game as well and re-initialize the connection to CoD servers to get NAT status to update.
Also - you can get moderate NAT type by connecting to a VPN using the Hybrid VPN config and adding your console.
I will echo what @l2eactionz says about moderate NAT type feeling a bit better in terms of "fairness" and what others have said here and on other threads about the better I make my connection / lower my ping the worse my experience is. I understand this is the exact opposite of what the Duma hopes to accomplish but the reality is gameplay just does not seem to be better this way.