39+3 - 60% effaced, 0 cm dilated!

I had an appointment Friday and I was high, hard, and at a 0. I went back today (Tuesday) and I was 60% effaced, but still at 0 cm. Baby is due Saturday (the 28th), my next appointment is Monday (the 30th), and if baby isn't here by the next appointment, they are scheduling an induction. Anyone have any success stories with having a stubborn cervix and going into labor on their own? Really don't want to be induced, but I don't want baby to be super late either. 😩