Stressed to the max

I'm 38 weeks 5 days pregnant (FTM) and would normally just be happy with letting baby come on his own. However, my husband and I have been in the process of trying to close on our first home for over 2 months and have just ran into problem after problem and now finally have a closing date of September 4th...which is the day after my due date. I am so scared that unless the doctor induces me a few days early, (I'm thinking the 31st) then baby will come around the time of closing and I'll be stuck in the hospital and we will have to push the closing date back yet AGAIN. We tried rescheduling the closing date and they said they could schedule it for 2 weeks later which would then cause us to have to pay a full month's rent at our current place rather than a week's worth (we currently live with roommates and that was the deal we worked out with them). We also tried asking if just my husband could be at the closing and I apparently HAVE to be there, no exceptions. This whole situation is just so stressful I'm literally losing sleep over it. I have had a perfect pregnancy with no complications so I'm not sure if my dr will agree to induce me 3 days before due date..I will talk to him at my appointment Thursday. I know there is still a chance that baby could come several days after his due date and after closing date but the chance is just too great that he will come when we are supposed to be at the lawyer's office signing papers. Ugh I'm so frustrated!