Good reason to get membranes stripped??

I'm 38 weeks pregnant. I was in the hospital a few days ago because of contractions every 3-5 minutes but was sent home because I had no cervical change in 45 mins. I'm currently 1 cm and 70-80% effaced (as of a few days ago. Getting checked again in a few hours). However, my doctor doesn't usually start stripping till 39 weeks. BUT along with all this I'm quite concerned I'm going to have a too big baby. At birth I was 11 pounds and my SO was 10. My stomach was also measuring 38 weeks when I was only 36 but then back to 37 the next week because I had suddenly dropped. I want an all natural vaginal birth and I'm really scared of him being too big for me to deliver. (I'm quite small and only 5'4) is this a good enough reason for my doctor to try stripping me now?

Vote below to see results!