My sister had GD and she went into spontaneous labour at 40+11 (or 12?). She was very strict about her diet and managing the GD, though it does get harder and harder near the end.

Every time the OBs at her hospital tried to medicalise the birth she just brushed them off "Of course I'll still have the baby at the birth centre", "Yes this baby probbaly is big, my first one was and I birthed her fine", "No, I'm perfectly happy going to 42 weeks thanks" etc. Educate yourself and just state calmly what you want to do. When you're actually stating the safest things for mother & baby then my sister found at least that the OBs never argued with her. She said they seemed a little bemused at times because normally the the conversation would go "You need to be induced" "Oh, okay". They didn't mind her saying she had other plans, but you need to state them and not take everything the OB says as fact.