Emergency AP is for exactly that...an Emergency !!
I understand that it is important that you complete the exams in order to complete your Phd but in the eyes of the USCIS, while this might be something that would warrant being issued a regualr AP document, I fail to see how you will convince the USCIS, even with the use of a your congressman, how this is an unplanned, unavoidable emergency.
I agree with Kezzie that perhaps some more forward planning would have avoided this situation from arising. It can't hurt to contact your congressman but I wouldn't hold out too much hope that they will be able to help you too much.
Mark