Aren't saddlebreds one of the breeds you can keep the main long and braid it in a running braid?
And even though a horse doesn't necessarily have nerves in his mane area, she may have something bothering her in the neck itself when you go to pull...brushing doesn't usually cause the neck itself to move, but pulling does...so maybe there is something wrong there? I would imagine it would be in the muscles on the top side of her neck.
She could also have had some previous experiences where pulling was not done gently; I've seen people pulling manes, and they shift the horse's entire head and neck when they pull! Can you pull her mane with your fingers? I know it would take alot lot longer, but it could keep her calmer, because the association, for the time being, is not on the comb used for pulling. Get some of those grippy finger things that mail people use to sort mail with; that would give you more grip to pull with.
As far as the clippers, have you tried various styles of clippers? There are super quiet cordless clippers; she may just not like the particular 'buzzing' sound that a normal clipper makes, as it does sound like bugs, when you think about it. I know there's a huge difference in sound between my cordless Andis, and my other corded 2 speeds. They are alot quieter than Oster, and others, but there is still a noticeable difference.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."