I'm sorry I haven't had time to read through the whole thread.
I thought I would share my birth anecdote, although I don't think there were any insurance coverage issues (it's that his malpractice insurance won't cover breech, right?) in my situation.
My twin B had been pretty insistantly breech for the third trimester. He was the larger twin, too, and according to the u/s techs baby A was pretty spread out (even though he was smaller.) I went for some Webster chiropractic sessions (this very successfully turned my first child, who was breech at term) but for whatever reason it just didn't seem likely to work this time around, with a different chiropractor and the particular positioning/space situation.
If twin B was breech when I went into labor, my OB was planning to attempt an external version after baby A's birth.
I went into labor at night on the weekend, and the on-call doctor was not my regular OB. The on-call physician came into the room after we arrived, introduced himself, and recommended a cesarean delivery for the second twin, because he was breech.
At this point, I spoke to him about what my doctor had intended to do, and also said that none of the perinatologists we'd worked with (at a different hospital an hour away) had seemed to think planning a vaginal birth with a breech twin B was outrageous or a bad idea. (I think the policy at that particular hospital would be a breech extraction for the second twin.)
I had a big problem with consenting to an automatic c-section. I said that I wanted to see what happened after the first baby was born....maybe the second twin would turn vertex, given opportunity. If not, maybe assisting him with an internal version would work. Why plan a pre-emptive c-section when we didn't even know what would happen?
The doctor said he wouldn't consider an external version at all (I forget his reasons, but he seemed to think it was a really bad route, despite the fact that his colleague had been planning to attempt one -- I don't disagree with that, actually, and hadn't really wanted my OB to attempt one right off the bat), and he responded to "the perinatologists at the other hospital" bit by sort of poo-pooing their practices (without actually doing so. It was the vibe. Sort of an, "I'm from a little town called Los Angeles, and around there, we think...." wink-wink kind of minimizing of whatever standards were governing protocol in the upstate NY hospital with the perinatologists I'd referenced. Obviously, they weren't as current or up-to-date as those in the little town called Los Angeles....ugh.
In the end, he basically said since I was refusing the c-section, he would do a breech extraction. I don't think we actually got to the point of stating that clearly (I'm pretty sure he was going to return to the discussion with me), because they suddenly realized I was complete and ready to start pushing and all conversation halted. I remember wondering where we stood, but after the first twin was born I heard him tell someone he'd agreed to a breech extraction.
So he was preparing for the breech extraction but the baby turned, instead. (I was upright when the first twin was born, so I took a good bit of time turning around, getting down, and getting into position for the extraction. All the while, I was telling my baby A how to turn, which I'd been doing for weeks at the end of the pregnancy, too. But at that point, it was "Now's the time, baby! Head down, facing back, chin to chest.") There was very little the OB had to do to turn him, though I think he reached in and helped in some way (I didn't feel anything at all, but I asked when I saw the doc a few days later and he said, "I turned him." But he also mentioned that the baby was turning, and he "reached in and turned him" so I think whatever happened was not heavy-duty wrangling.)
Anyway, I'm sharing this because I had an ostensibly "current" doctor (in town, he's considered the "young, up-to-date OB who is very competent but not always the best with his bedside manner") who spewed all sorts of studies findings contraindicating versions & extractions, and was recommending automatic c-section for the second breech twin.
I don't think your doctor is necessarily coming from nowhere with this.
As far as hospital policy, they don't do breech deliveries. With multiples, if the first twin is vertex, the "vaginal attempt" is "allowed" but I think the second vaginal birth only will happen IF the second baby turns. (Unlike the other hospital I mentioned, where breech extraction is standard.) With my regular doctor, though, if the second twin could not be turned, she would have opted for a c-section (she never offered me a breech extraction or any kind of breech birth.)
I had gone into it believing my baby would turn when he had the chance (I honestly didn't believe the external version was going to be needed and I think I'd have asked her to wait, though not sure how that would have all gone down), and not thinking that I would end up with a c-section. But I guess I knew if things went wrong or he just didn't turn, or if he got into a stubborn transverse presentation or something, c-section would be the result. In the end, I think the on-call OB was assuming breech extraction as the default, probably because I had refused a c-section (at least, a planned one) and it was so late in labor that maybe they could claim a breech extraction was unplanned? Or that it was done only because I refused the other procedure?
I'm sorry I'm rambling so much.
I wonder if your doctor would consider making the decision after the birth of the first twin, when he can see what happens with the second twin's positioning. You may not be able to push him to deliver the breech twin, and he may not reconsider his misgivings about external version or internal version, but maybe you could clarify that rather than an elective repeat c-section, you would like the decision made in the moment because of necessity ("necessity" in this situation, of course, being debatable) rather than planned from the start. Perhaps the baby won't need a lot of manipulation, or any manipulation. You understand his policy against breech delivery, but is he willing to consider any alternatives or allow that there are possible scenarios that would make a c-section completely unnecessary?
(Sorry if you've already gotten past this point and are no longer dealing with him. Like I said, I didn't read to the end of the thread.)