a coworker of mine has a persian and every year or so she has her shaved completely as the mats become too much for her and the cat to deal with.

I'd have her shaved and start from there, like you said.

One of my cats was hit by a car and he had numerous lacerations where they stapled him up. I think as a result his skin is full of scar tissue that makes his skin very sensitive and he HATES being brushed. I think he actually hates anything near his skin because he doesn't even groom that well to the point he'll have mats (he's short haired).

Anyways, long and short, he hates being brushed. He does tolerate the Zoom Groom, which is this soft plastic pronged brush thing. It gets the undercoat out, but you should get the mats dealt with first.