There's no silver bullet, but it can't be hard to do better than a nine-digit number you reuse everywhere and is almost impossible to change.
Possible solution advertise all SSN's in card format invalidate them all and force hand of government? Implausible but not improbable.
Or possibly advertise your own once it is known to be hacked...just throwing wet spaghetti at wall but there may be something that sticks.