Unfortunately, until this exact scenario happens to someone, we won't know. And even then, we may not get solid info. Disney has made it known that exceptions will be handled on a case-by-case basis. What one CM allows you to do in this situation may be different than what another CM allows someone else to do in this situation. There are no real answers to "how will Disney handle situations out of my control?" because each situation is unique.
Basically, you plan the best you can. If something goes wrong and you end up late for your FP window and a CM says, "I'm sorry", then you have the choice of either asking for an exception or hopping over to the standby line. If you ask for an exception and the CM listens to your situation and says, "I'm sorry", then you have the choice of asking for a manager or hopping over to the standby line. And so on up the line.
Look at all the people on the DIS who were not even aware they COULD use FP past their stated times. Those folks managed to make it through WDW just fine, real life situations and all. I'm sure it won't be nearly as much of a problem as so many people are making it out to be.