You also need to show that this is an emergent situation. That is, why the situation is not a result of poor planning and not applying for AP sooner.
Don't count on this - they use a very high standard of the definition of an "emergency" for this purpose, unfortunately.
If the AP is well past the processing time, try following up the application as well, through congressman, explaining the situation you are in. Maybe they will decide your plight is bad enough and follow up with the service center.
~T