You are so close. I remember when I was where you were at (not that long ago) and I was so ready for the babies to be here. My body was just done.
A similar thing happened to me. At first my dr wouldn't schedule a csec before 39 weeks (I about cried when they told me that) because that was normal - but it is normal for singleton. Then when I got to 35 weeks and some change, my dr called the university hospital and they told her it was safe to deliver me at any time from now on. They decided to schedule me for 37 weeks because that was optimum for twins (37 - 38 weeks is when twins are supposed to be the most healthy according to the university hospital). I was having contrax and my gd went away signaling the placentas where starting to die so they decided to go a head and do the csec that day.
Are you having any contrax? Even if the csec isn't scheduled early, you still may have them in Aug.
Best of luck with your decision!