^ Obligatory long post cat picture.
TL;DR: A big thanks to the mostly drunk testers last night, I have a much better understanding of the Civ 5 matchmaking system because of the troubles we had. We can now try to troubleshoot connections between players in Civ games or/and try pitboss matches using one of the TSA servers.
Thanks to everyone last night that took part in what was meant to be a Civilization match which we would have enviably played for 4 hours then abandoned and never come back to like all of the best matches, but unfortunately turned into a night of testing, drinking, sadness, banter, and Garry’s mod followed up by Cards Against Humanity, also like some of the best Civ matches. 
Still I hold to the fact that Evolve is both an extremely useful program for us to have, not only for Civ 5 but also for the plethora of other games that work better/only work in LAN mode. It just has a few kinks to work out, which last night went a long way towards solving.
Main Problem:
Civ 5 seems to rely on every player being able to communicate with each other (peer to peer system) rather than every player only having to being able to communicate with the central host who then relays information out to everyone (client to server system), the system makes sense for the vast majority of users but does advertise the need for Civ5 to support dedicated servers better (more on this later).
This brings me on to what the problem last night was, for almost every match we had at least one problem players, someone who had something blocking their connection to someone else, this manifested as a player appearing without their name or not at all in the lobby, preventing the game from being played until the connection issue was either resolved or they left.
Solution One:
This problem is not just in the LAN games, it’s also in the normal internet games, just to a lesser extent. We’ve experienced it before lots, games stop working until suddenly a player loses connection then it starts working again perfectly, that’s because it’s always down to the one problem player.
Naturally the first solution would be to fix the connections between the other players and this problem player. Evolve goes a long way to doing this already by connecting computers together as if they were in a LAN, we just need to fix the things that are blocking Evolve (likely firewalls). We even have a starting point, it a player can’t see someone else’s name in the lobby then the problem is between the connection of those two and we can start troubleshooting from there.
Solution Two:
I said I’d talk more about dedicated servers and now I will, Civ 5 supports dedicated servers in a limited capacity for one mode only, pitboss. Pitboss is a mode intended to be played like a long distance postal chess game, players can drop in and out whenever and will get an email notification when it’s their turn again.
In theory I should be able to host a game of pitboss on one of the TSA servers therefor bypassing the issues that people have when connecting to each other.
