When I told my midwife I was induced at 10 days past my EDD, she said "oh, that was early. why didnt they wait until you were full term at 42 weeks?"

She said that there is no greater risk in going to 42 weeks than having the baby at 38. She said this was well documented so there should be some information out there.
They should be able to monitor placenta function as well, with an u/s.

Maybe you can compromise along the lines of you will go by their dates as long as you can get to 42 weeks before discussing induction, that should put you somewhere in the middle.

Are you happy to be monitored for placenta function if they determine you're post dates - if you are then ask for that.