All I'm going to say is, you can do this. A baby who has not yet dropped is a baby who is not yet ready to be born- if they try an induction, you WILL end up with a section, especially with a first.
My firstborn weighed in at 14 lbs, was born vaginally at home with the aid of a good midwife and as near as dammit fell down the toilet
He did, admittedly, have a relatively small head (50th centile- for length and weight he was off the scale) Fat is squishy, as has already been pointed out, but IME a long baby will take longer to engage fully in the pelvis- this is based entirely on anecodotal evidence, because as far as I know there's been no studies done BUT the later babies were the long ones.
So, the question is, how stroppy are you prepared to be? Are you going to fight with this midwife, or are you going to go looking for a replacement?
OH- fwiw, I don't believe in the existence of gestational diabetes, at least not in terms of producing large babies (if, otoh, you had any symptoms, that would be different). If some stupid doctor trying to defraud insurance companies by ordering unnecessary tests chooses to think that a GTT is a good idea, let him- there's a reason why most countries with state-funded healthcare don't bother with them (i.e. they're inaccurate.) I have big babies because I have a big bottom and child-bearing hips (i.e. a fat ass), inherited from generations of down-to-earth, baby-birthing, hard-working women who didn't have time for all this namby-pamby nonsense with ultrasounds and medicine because they had lives to lead and jobs to do, unlike dumb quacks. Oh, and I'm only 5 ft 3.
I'm really sorry this is happening to you, but somewhat angry on your behalf.