Early Induction=Terrified momma. need advice

This is my fourth pregnancy. I have just been diagnosed with Cholestasis of Pregnancy... which means there is excess bile in my system due to an abnormality in the function of my gallbladder and liver. This will not harm me (except an INSANE itching all over my body) but It causes problems for the placenta. So my Doctor is going to induce me at 37 weeks. If they dont induce the chances of stillbirth increases drastically. but they wont induce me before 37 weeks because they want to give baby as much chance to develop his lungs as he can have. I am going in 2 times a week for a non-stress test and an ultrasound to make sure baby is growing and the placenta is functioning correctly. If at any point the baby is in dis-stress they will induce me before 3 weeks.....  the doctor was explaining all of this and then she said that my chances of needing a c-section double because with this condition the baby might not handle the stress of labor well... especially if they induce before 37 weeks. My question is.... is there anything I can do to make sure my cervix is ready at 37 weeks? I googled ways to naturally induce labor but it seems to me that is for women who are term. I hate that we have to kick him out early:( but I want to make sure it is as safe as it can be and I want to do everything in my power to not have a c-section. HELP! anyone have any suggestions on ways to make sure my cervix performs when asked? The doctor said that because I have given birth vaginally 3 times before (the last one was 6 years ago) that the cervix will probably remember what it needs to do and it will be fine... but like I said... I want to do whatever I can to deliver this baby naturally and vaginally.