Getting her inside was the hard part. When we tried to get her up the steps onto the deck, she just flopped down on the ground and we had to lift her up. We finally got her into the nice air-conditioned house and onto the comfy sofa and she just totally relaxed. Her wool was MUCH thicker and it took quite a lot of work, but she just laid there quietly while I trimmed almost 2 whole sheep off her. She no longer looks like a horta.
After I finished getting as much as I could off with the electric shears (and they remained intact the whole time), we used scissors to carefully trim around her more sensitive regions like her face and udder. She just laid there with her head on my lap, apparently enjoying the breeze from the fan. She eventually fell asleep. Even after we finished, she just laid there on the sofa in the nice cool air, with no flies bothering her. She didn't feel the least need to get up and go outside. I got some sheep candy and she eagerly ate out of my hand. She only reluctantly got up to leave after Oberon climbed up on the deck and started bleating loudly outside the door.
All the sheep are sheared and in the nick of time too; tomorrow is supposed to be in the 90's and they'd probably have overheated.
I took some pictures of the enormous wool pile and the blissful, much skinnier sheep, I'll post them later.