[kasnavada]

Wouldn't it be better to name the games whatever_001, whatever_002, whatever_003 and so on ?

The list is shown alphabetically I think. This way, you get all turns in order instead of having a list that looks like this : 1, 10, 100, 101, 102, 103, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20 (...). So you could using this have an entire game in the right order.

Windows (?) trick :
Another idea would be, after every single submit you make to copy-paste the game folder. Windows uses for a game called 'Blitz' the name "copy of blitz (1)" and increments the number for every copy (the exact text will change according to your language and OS though). Once the game is finished you just need to rename the folders. Tip : Vista and XP allow the renames to be done in "group", if you select all "copied" folders, delete the "copy of" part, it will be removed from all selected folders.

An equivalent should be on mac and unix, but I don't know those systems that much.