I think I have a similar or even the same problem.
I did several tests and now I'm very sure that it is caused during loading and not saving.
Almost every time I try to load a safe during a game, the safe-file grows after saving again (minimum 4MB more).
After doing this a few times, the loading-time becomes longer and longer, the game even freezes or crashes (problems like they're described in the posts before).
If you create a new game during an ongoing game, the new safe instant get's big (about 10MB).
If I restart (really, restart it, just changing into main menu is'nt enough) the game on the other hand, and load and safe then, the file just grows about 1-3KB (tested it around 500 times...).
So I would guess the memory of the safes is'nt fully or correctly cleaned if you load a safe.