I'm going to try to be a little computer-sciency here with a discussion. First off I am making two assumptions here that could be completely false - so a dev could come in here and completely destroy my points.
Assumption #1: The NAT Negotiation server is getting bogged down and having a hard time processing all the requests in a reasonable amount of time.
Assumption #2: Every connection between two players goes through the NAT Negotiation server.
Ok with these two assumptions, heres the new scenario I would propose to decrease the load on the NAT server and help with its scalability with more players. Here is the a description of what could happen.
1. Player A hosts a game.
2. Player B attempts to join the game. Player B and Player A use the NAT Negotiation server to properly forward their UDP packets so they can form a peer to peer connect to eachother.
3. Player C attempts to join the game. Player C and Player A use the NAT Negotiation server to properly forward their UDP packets..
4. Once connected, Player C uses Player A as a temporary NAT Negotiation server to connect to Player B.
5+. All new players connect to Player A first through the NAT Negotiation server. The connections to the other players happen through the host (Player A).
Conclusion: This makes the requests to the NAT Negotiation server of order n (n=number of players) instead of n^2. This would reduce traffic to the NAT servers by about 6 fold (if you assume a 3v3 is an average sized game).
Another possibility with this setup is to allows players to join the lobby once connected to Player A. Then Player A can function as a simple chat server between players. This could also allow Player A to boot the people who are failing to connect to other players.
Essentially, use a hybrid client-server for setting up the game, and switch to peer-to-peer when the game actually runs.
Anyway, I don't know if any of this information is useful at all, just an idea that came to mind, and the forums are public, free spaces, so I threw it out there to see if it's at all helpful.