Had a sort of similar situation, but not an obstetric patient. Called to ED to intubate patient with combitube in. I arrived, patient was 45, had massive MI, EMT unable to intubate in field so placed combitube. Pt was morbidly obese, BMI probably around 45, apple shaped female with short neck, also large tongue protruding around the combitube. However, in this case, the patient was near coding. She was blue, and they were not ventilating her, and there was food coming out of her mouth... I grabbed a fiberoptic, intubating lma, and glidescope, and suction. Pulled the combitube out, suctioned, and was actually able to intubate easily with a miller 2. I definitely got lucky, but this patient was in more extremis. She ended up coding and dying shortly afterwards anyway.
I agree that this patient probably needs a more definitive airway before the section. Whether I would proceed with the combitube probably depends on the reason it was placed in the first place. Was she obese with a bad airway, and there was a failed intubation attempt? Versus that is what the EMT had on hand? Also, the fetal heart rate is okay for now. And moving her from the ED to a csection OR table could displace the combitube. Also, turning her on her side for a spinal could displace the combitube as well. You probably have the luxury of enough time to assemble an ENT on standby for a trach, while you have all your airway tools at the bedside to try to place an endotracheal tube.