Hi, Tracy! Great questions!
I'm so glad you are trying to think through this and not just take everything your doctor says for gospel. No one cares more about you and your baby than you do, even your doctor. Studies show that for most babies, an induction prior to 39 weeks is detrimental to the baby's health (See an article from the Wall Street Journal online.wsj.com/.../SB10001424052748704615504576172291331227676.html)
And of course unnecessary inductions lead to a much, much higher risk of cesarians, which have their own risks and long-term affects on the both the mother and baby. (For some of these, see www.americanpregnancy.org/.../cesareanrisks.html)
Especially in your situation, your A1Cs are very close to those of a non-diabetic woman, who would not need to be induced early. If I were you, with such great A1Cs, I would push to let the baby decide on its own when to come. If your A1Cs were in that range without you having to work to keep them there, the doc would most likely not even consider you high-risk
Your doctor, most likely, is operating on old information, the time when diabetic moms could not keep such good control as you have been, and thus is still using the blanket "we always induce diabetics early" approach. Diabetes alone is not a good enough reason to induce early these days of CGMs, pumps, and near-normal A1Cs that hard work can accomplish. (Actually, you are likely more healthy than a non-diabetic woman because you haven't been stuffing your face, satisfying all your cravings like they have!)
Also, it's you and it's your baby, not the doctors. He is there to help and give his professional opinion, but it is up to you to decide. You are paying him, so it is up to you. (As long as he doesn't "fire" you as a patient.)
Here's the only problem: if the doctor wants to induce you early, he may be tempted to find a reason. He may agree to let the baby come on its own "if all is well", and then tell you around week 38 that such-and-such is a problem and that the baby needs to come right now. You'll never know whether that's the truth or not, so you'll give in to the doc just to make sure.
If I were you, I'd either go with an independent midwife and a home-birth (if you can find one that will take you) or just go along with what the doctor says.
Here's my story:
I found a doctor who said he'd let me go to 40 weeks, but scared me with the possibility that the baby must come sooner. My control was not nearly as good when she was conceived (7.6 A1C, with subsequent A1Cs of 5.9 and 6.2) so I was getting a little worried too.
But I hated the idea of cytotec and pitocin and just laying there in pain for hours without being able to move around during labor, and I was trying to do the whole natural birthing thing. Trying to get the best of both worlds, but I think I got the worst of both instead.
I scheduled the induction 2 days before her due date, but breast-pumped my way into labor two days before that. I also took some castor oil (DON'T take castor oil!). I got my contractions going enough that I couldn't sleep through them, so I was already very tired by the time I got to the hospital at 8:30 in the morning on induction day. I was 3cm dialated (from 0 a few days before). The doctor overseeing my labor knew I didn't want pitocin, so she let me labor mostly on my own all day. She broke my water around 12pm I think, maybe later, and there was meconium (baby's first bowel movement) in the amniotic fluid, which can be dangerous for the baby to drink in. (I was still 3 cm).
I continued to labor all day until about 10pm or so, the doctor checked me again, still 3cm, so she said let's start pitocin. I was exhausted by this time. Had been in labor for 2 days with little progress to encourage me and little sleep. The fetal monitor said that the baby's heart-rate was dropping too low for too long during the contractions though, so she said "We need to do a c-section". I was actually happy about that at the time because I was so exhausted.
So we did the c-section, which was quite traumatizing for me. They don't let anyone come with you while they put long needles up your back for the spinal (or epidural). I was shaking all over, laying naked in front of a bunch of strangers whose faces were covered with masks. They put a catheter in me, which my doc made me keep for 24 hours (still no idea why), blood pressure cuff on that went off maybe every 10 minutes, and cuffs around my legs that squeezed every few minutes (and all through the night while I was trying to sleep too). They tied my shaking arms down, and finally my mom and husband were allowed to come in. (They usually only let one person in). I was relieved when I stopped feeling contractions, but there was a lot of pushing and pulling pressure, especially when they pulled my baby girl out.
I cried for joy when I heard her for the first time. They showed her to me briefly, then she was whisked away for her bath, APGAR testings, etc. while I got sewed and stapled back up. A bunch of my in-laws witnessed her first bath and check-up, but I, the mother that went through months of carrying her, and then the labor, did not.
I got to hold her before going to bed that night, and breast-feed. She latched right on, no problem the first 3 times she tried. In the morning though, they said she had an infection and had to be kept for 24 hours on antibiotics, possibly 7 days. They would know with more tests how long to keep her. When the tests came back, however, even though the results were good, they still needed to keep her for such and such a reason (I get the feeling that only 24 hours was never an option- they planned to keep her from the start). So they gave her some bottles and pacifiers when I couldn't be there to nurse her, which meant she struggled to nurse for the first few weeks.
I think the infection was probably due to her swallowing the meconium that she passed, which was due to the castor oil that I took to get labor going "naturally".
As for me, everyone said I bounced back quickly (for a c-section) but walking down to the NICU for 7 days was incredibly painful and I had to walk slower than a 90-year-old grandma. Coughing, laughing, and sneezing all shot fiery bolts of lighting through my lower abdomen, causing me to avoid those activities at all costs for like 3 weeks. I have a big ugly scar and belly fat that won't go away even though I've lost all the baby weight now, plus about 7 lbs. more. (I weigh about 120).
By the way, my baby girl was 7 lbs. even, 20 inches long, and had APGARs of 9, 9, and 9. Her blood sugar never dropped too low, and she was strong- could hold her head up for a couple seconds from the day she was born. I feel confident that she would have been perfectly healthy if we had let her come when she was ready.
So anyway, long story to say: either do it your doctors way, or go all-natural and wait for the baby to come when it's ready. (But at least wait for 39 weeks!) And whatever you can do to avoid a c-section is worth it. As a diabetic, if you have a c-section, you will probably never be allowed to give birth any other way. I am going to push hard for a VBAC the next time around, but I'm not too optimistic.
Good luck, and remember, no matter what happens, you have done your very best, with the information you have, to give your child the best start in life! No one can ask more than that. And 99.99% chance your baby will be born healthy, beautiful, and strong. Good luck and God bless!