Dr. has me scared!

I'm overweight (364lbs) and 5'9. I've only gained 14lbs my entire pregnancy and have measured large for my fundal heights since forever (in my opinion and 2 of my doctors' opinion because of belly fat). At my last appointment the doctor in my practice who is "a friend of c-sections" said he thinks this baby is huge and scared me with talk of shoulder dystocia. I have a 4 year old at home (born vaginally 8lbs12oz no complications, induced at 41weeks) and do NOT want to do a csec recovery. A second doctor in my practice ordered a growth scan (at 40 weeks to the day) and they're saying the baby is measuring to be 11lbs 4oz!!! ( + or - a pound!) this second doctor (whom I prefer) gave me a pelvic exam and says she thinks I have room in my pelvis to birth naturally. However, now I'm concerned that I won't be able to or will hemorrhage either way (vaginally or surgically). Any advice? Thoughts? Help? I want c-section to be a last resort so she's willing to let me try to labor - being induced Monday morning 6am.