I'm not aware if Most Wanted takes it's file saving architecture from previous games or not but The Run had the same issue for a small number of players on the PS3. If I recall, the issue was popping up with PS3 Slim and could have been as a result of some interaction with the firmware. Sony puts game stability improvements in most of their firmware updates. I recommend updating to the latest issue if you haven't yet. If that doesn't work then try contacting them to see if they've considered issuing a stability patch (although you're not likely to get the response you'd like but it never hurts to ask).
I honestly don't see how replacing the harddrive would be an issue but an old drive might very well be picking up bad sectors as a result of it's age. The only way to bypass that ... To be honest I can't think of anything that'll let you bypass that since you likely can't start a new game and have two saved game files without creating a new user account on the console. Essentially deleting the file will free up the space where the error is but since the PS3 doesn't have physical management software for bad sectors (as far as I'm aware) you'll just end up saving any new games in the same physical space and the issue will pop up again.
I hope at least some of this will help you.