Baby still sitting "high" at 40 weeks?

Jen • Pregnant with #2 ❤️ Due June 13
Hi everyone, I'm 40 weeks tomorrow and was checked yesterday by doc. Baby's head is still "high" and no dilation. I'm being induced on 41 weeks due to GD even though it's controlled. When did your baby engage/drop? She's up so high it's hurting my ribs, and I'm worried that if she doesn't drop and it comes to my induction date that it will make my chances of C/S higher. Were you told your baby wasn't engaged at 40 weeks and everything turn out alright with vaginal delivery?