Here is how I am handling the multi-player saving issues.
1) Set Autosave to 1 turn. These save files are located in /My Documents/My Games/Sid Meiers Civilization V/saves/multi/auto
2) Save the game manually using Ctrl-S. This save file is located in /My Documents/My Games/Sid Meiers Civilization V/saves/multi
3) The only directory that Saved games can be loaded from is the auto save folder. What you have to do if you want to load one that you manually saved with Ctrl-S is copy it into the auto folder, and then add "AutoSave_" without the quotes onto the file name. These are the only files that the game will read. This will then load the game lobby and you can send game invites to the people who were playing. They should load into the correct position in the lobby.
If you have any questions please let me know! I'm still learning this, but myself and 2 friends have managed to get this to work have decently.
Be careful that if you are playing several multi-player games that you either save with Ctrl-S, or rename the AutoSave file that you want to keep for each game, otherwise it may get overwritten.
Hope this helps others out there!
