Me and my friend have the same problem. We are playing BTS and have the latest patch and are playing a huge game by direct ip. It takes several minutes to transfer game.
The saved game is like 1,9mb... both have 10mbit connection it should be sent in a couple of seconds.
Seems like the transfer function in civ is really bad. There should be some kind of configuration to do to speed it up to connection max.
The game should only send the saved game then the other players civ should load it and then start.
I dont know if its much faster in the beginning of the game. seems its really slow when you just start the game and there is not much information to send.
I know in the old quake 2 game I played again online a couple of months it downloaded the map of the game i was joining with 2kb/s. Was just a configuration you had to type in and it started to operate at maximum speed and the map was downloaded instantly instead of like 10-15min and often got times out during that period. Should be something to do to speed it up in civ also.