Copying my reply to your support email, in case someone else has a similar problem, and finds this in a search:
Try clearing the cache, if you didn't so so when reinstalling the game:
- press and hold the Xbox button on the front of the console for 10 seconds until it shuts down
- unplug the power cable and wait 30 seconds
- plug the console back in and turn it on
- log into the same Xbox Live account you were using, start the game and let it sync, if required
It sounds like one or more of the saves is corrupt, causing the game to freeze when trying to read the information about the save data (date and time, playtime, etc). Unfortunately, the Xbox doesn't allow manually backing up or restoring saves, or even deleting them individually.
If you start a new game, can you make a manual save? Moving up the beach from the starting location can trigger an auto save, which might overwrite one from your current playthrough. If you don't already have an honour mode difficulty save, starting one would avoid that problem, since it uses a separate, single save slot.
If you start the game from a different Xbox account, if available, can you start a new game, make a few saves and open the save/load windows? That would give a separate hard drive space for saves, and if it works, would help confirm the issue was with the saves in your current playthrough.
Do you have access to another Xbox, where you could log in, start the game and have Xbox Live download just the latest save and make sure you can open the save and load windows? If that works, you could delete the local copies and try that from your Xbox. As far as I know, there is no way to confirm that saves have actually been synced online.
If the issue is with one or more of the saves, there is no way to selectively delete/replace them. Other than playing by only using quick and auto saves, and only being able to quick load, or load the latest save from the main menu:
If the corrupt save is a quicksave, eventually, or if you quicksave repeatedly, all of the current saves will be overwritten with new quicksaves, which will hopefully fix the problem at some point, and allow you open the save and load windows.
The same would eventually happen with auto saves, or more quickly if you started a couple new games on explorer difficulty and went though up to the fight before the gates of Cyseal.
Unfortunately, there is no way to delete/overwrite manual saves without being able to open the save or load windows in-game.