If a patient wanted to be induced early to avoid a difficult delivery of a large infant, how unusual will it be to induce at less than 36 weeks?

Extremely. No doctor should consider this based on current guidelines. You should be evaluated for causes of a large infant. Elective delivery should not be performed prior to 39 weeks. Estimated size is not an appropriate indication for early delivery due to the inaccuracy inherent in estimating fetal weight. Size may be considered when deciding the route of delivery.
Wouldn't happen here. Any doc trying to induce early delivery at or before 36 wks here would be kicked off the hospital staff and be at risk of losing his/her license. The incidence of premature lung disease approaches 50% at that point. Local guidelines exclude any elective delivery before 38 wks.