I wonder if people are suspecting you of being a troll because you claim to have researched this so thoroughly and yet seem blinded to all the complications of abdominal surgery - you only discuss the complications of vaginal delivery.
A few points I'd like to raise - in a normal vaginal delivery, the baby is signalling they are ready to be born. Usually this is because their lungs are mature and they are due. I rather feel this is important. Likewise your body is better geared up towards breast feeding.
You may be keen to retain good pelvic floor control but again, this is due to pregnancy as opposed to just the birth itself. Otherwise my pelvic floor needs to have a strong word with itself right now. By undergoing a c section you are at long term risk of hernias and adhesions - which can require pesky hospital stays and annoying surgeons having to open up your abdomen. My friend had an emergency cs 12 weeks ago. Her wound is still infected, still causing her pain and still impacting on her life. But you'll be back at work then?
The most upsetting thing I've found you to say has been that you have three months mat leave to recover. Really, it should be that you have that precious time to bond with your baby. The better you are physically following birth the better you can bond and enjoy the new life you have created.
You say you have a history of big babies. I can tell you having already delivered a 7lber and a 10lber I healed a lot quicker with my heavier baby and was up and about with much more ease. I tore both times, btw. They usually try to avoid episiotomies if they can as natural tears heal better.
Ultimately, as you say, you're prepared to pay for it. But to feel the NHS owes you a c section is wrong imo - budgets are there and cancer treatments don't always get approved. It's not just the cost of the initial surgery to consider, also follow up care, GP care for wound infections (friend is currently on visit number 4) and possible multiple hospital stays for complications, which can be recurrent and difficult to treat. Your abdominal wall is precious. Much, much better to keep it intact ime.
As a last post, I'll c and p one snippet of info I found on wikipedia I'd be surprised if you haven't come across in all your research, which for most mothers would cause some uncertainty over a choice to have a non indicated cs.
'Higher infant mortality risk: in c-sections which are performed with no indicated risk (singleton at full term in a head-down position), the risk of death in the first 28 days of life has been cited as 1.77 per 1,000 live births among women who had c-sections, compared to 0.62 per 1,000 for women who delivered vaginally'
Good luck with what you choose and what you can arrange.