Just to correct something:

That's actually not true for international bereavement fares (at least it was not true last March). The intl. bereavement fare is the lowest available fare to your destination on the day you need to travel ignoring any advance purchase requirements. The penalty for changing the flights are still determined by the fare you book - i.e. you can buy an S fare up to 2hrs before the flight, but you'll still have to pay $200 to change the return.