Update time!
She's more alert today than she's been- She's looking around and responding to sounds. I have been taking her outside for a while every day, but today she had no desire to go out and acted on that. She walked back in immediately and took a nap near the door. Her flock later ventured bravely onto the porch to say hi, and although she didn't get up, she did "chat" with them a bit through the door.
She still will only eat watery egg. She seems to like eating and drinking at the same time. I think she's eating a bit more, but that might just be wishful thinking. Her poops are still very watery and gross, as is expected of a bird who isn't eating enough.
Still not sure if it is egg peritonitis or not. From what I've read, it sounds like she would be wasting away more and more if that were the case. She is definitely not out of the woods yet, but she has shown slight improvement. And a lot of the telltale signs are simply not there, like the swelling.
Today I saw the first sign of something amiss in the rest of the flock. There was a big worm in one of the hen's poops. This was a surprise, as I wormed them all fairly recently. I used ivermectin, though. During the day's research, I have learned that this isn't actually an effective wormer for chickens. I'm going to order some valbazen and worm the main flock with it.
I have been getting very up close and personal with my sick hen's poops over the last week or so, and have seen no signs of worms in it, so I don't think she has a worm problem. I don't want to put her under undue stress by worming her, but if some sort of worm could be the source of her problems I want to get rid of it. I haven't read about worms causing her set of symptoms, but I might have missed something. What are your thoughts?