If a patient wanted to be induced early to avoid a difficult delivery of a large infant, how unusual would it be to induce at less than 36 weeks?
On face value, it would be very unusual to do this. The baby's lungs can be mature at 36 weeks, but 36 weeks is the center of a bell curve. Some babies do it earlier, some later. In my area, the standard of care is to not induce before 39 weeks unless there is an overriding danger to mother or infant. In fact, induction just for convenience at 39 weeks is legitimate if the cervix is inducible ("ripe"), usually a function of some dilatation and effacement (thinning) already. There is something called a "Bishop's" score that takes into account dilatation, effacement, and whether the cervix is lined up with the path along the birth canal. A "favorable" Bishop's score should be evident before considering induction for convenience.
But at or after 39 weeks.
Of course, I don't really know all of the details here, and I assume that there are other reasons for a doctor's decision to induce that early. Besides the medical indications for delivery early, like Pregnancy Induced Hypertension, diabetes, bleeding, etc., there can also be reasons you won't find in any text book. If there were a psychologically damaging traumatic delivery in the past, an earlier delivery's benefits for the mother may outweigh the risks to the infant. Or if there had been a fetal death at or around the due date, I can understand a mother's desire to get a known prematurity situation out into the outside world than worry about the unknown chances of another tragedy. What if the mother had had a very large infant in the past that so damaged her that sexual intimacy was only re-acquired after extensive surgical repairs over the months or years after?
In other words, the text books and the "standard of care" apply to the "standard" text book patient, but since every patient is different, a doctor must also use judgment in deciding how far he or she can stray, based on what's best not just for the mother, but the mother AND baby. The art of medicine is the latitude in fuzzy directions away from this standard.
But it need not be such an anguishing decision to "unload" early. Amniocentesis can determine if a baby's lungs are mature. If they're not, then this has to figure heavily into the risk vs. benefit formula. It they are, then a delivery can be legitimately and ethically effected earlier than the "legal" 39 weeks.
In my practice, if the mother or the infant is in real danger, delivery is indicated. If there's no imminent danger, but it's a matter of misery before 39 weeks, I usually insist on an amniocentesis to assure myself before committing to an earlier delivery. But in my world, misery that severe is very rare. Almost all of my patients are good sports about the "terminal miseries of pregnancy" and hang in there. Not wanting a Cesarean delivery is not usually an indication for early induction. And fearing the worst based on estimates of the baby's size can be jumping the gun, because even with the most accurate ultrasound measurements, the baby can be overcalled by as much as a pound.