The end is in sight. He basically said that in this day and age, you can express a preference for a c-section and, frankly, you can demand one. That being said, the c-section isn't off the table just because they're both head down. He had told me and Mike at our last appt that we should just ask the u/s doctor for his opinion on a 36 1/2 week c-section (which would be 6/20 or 6/21) without an amnio. (The amnio checks the development of the lungs to ensure that they're done. Typically the lungs are ok at that late stage in the game, which is why he wanted us to ask about his opinion without an amnio at 36 1/2 weeks.)
The u/s doctor said that 37 weeks is always better than 36 1/2. He wouldn't object to 36 1/2 weeks though with an amnio. Going with that, my doctor took the 20th and 21st off the table and went with the 22nd without amnio, which is a Friday, where I'm 36 weeks and 6 days. A Wed or a Thurs would have been more desirable to try to work out with Mike's new employer, but a Friday will just have to do. He can miss a Friday and a Monday just as easily as he can miss a Thursday and a Friday.
So, there it is....as a last resort, I won't be pregnant anymore by June 23rd. I still could go naturally earlier though.