Hi everyone. So, at least for now, it seems like the situation has been resolved.
I took Isabel to the vet yesterday. He initially wanted to reinsert the tissue and put two stitches to keep it in place, but after examining Isabel, he noticed she had an egg she hadn't finished laying, which was a big additional complication. He said it was important for her first to lay the egg, and then they could reinsert the tissue. The vet planned to start by giving her an injection of Metacam to deal with any inflammation and Oxytocin to see if Isabel might lay the egg sooner. The vet asked me to leave Isabel at the clinic for the day and pick her up before they closed. When I picked her up, she still hadn't laid the egg. The vet said to call first thing in the morning to let him know if she had laid the egg. On the car ride home, I heard her chirping or whimpering, and a large red mass came out of her as if she was trying to lay the egg then, but that red mass for the most part went back inside, except for the small lump. When I got her home, though, she seemed relatively normal. The red lump was still outside, but it wasn't any more protruded. During the afternoon and evening she was eating, preening, and perching normally.
Today in the morning she still hadn't laid the egg, so I called the clinic and updated them on the situation. The vet said to bring Isabel to the clinic immediately. The staff asked me to leave her at the clinic and that they would call me later after the vet examined her. Several hours later, the vet called. He said that they had waited in case Isabel might relax and lay the egg, but that didn't seem to be happening. So the vet first attempted to gently massage the egg out, but that made Isabel more stressed and he noticed the egg was going further in. He said they sedated Isabel, and then were able to collapse the egg and extract it. Once the egg was out, the tissue went back in by itself. The vet said there hadn't been any need to use stitches. Since she's been laying so many eggs, the vet had been worried that she might try to lay an egg while the stitches were in place and before it was time to remove the stitches, which would prevent the egg from being able to pass. So it seems positive that there wasn't any need to do so. The vet said that Isabel was doing well after the procedure, perching normally and somewhat relaxed.
The vet said it was hard to be sure about the size of the egg because they had to collapse it, but he seems to suspect that it was an unusually large egg that has possibly pushed out the red lump and Isabel was having trouble laying it.
The vet asked to keep her at the clinic just to make sure everything is okay until later in the afternoon. He did recommend Metacam for a couple days, but since Isabel has always been the most skittish of all my parakeets, and considering that she might be more fragile after all this, I'm not sure I'd be able to administer it. I know for certain she would resist, because when I need to move or transport her, she'll throw herself against the walls of the cage to avoid me and generally panics. The vet said they could give her Metacam by injection, though it would only be in her system for about 24 hours. He doesn't think there would be too much of a negative consequence of not administering the Metacam for more days.
So that's the situation so far. I'll be picking up Isabel later today. Again, I'd really appreciate any insight or advice. It seems like the situation has resolved in one of the better possible scenarios. They were able to extract the egg without any problems and they didn't need to do a more aggressive procedure. I don't think we're out of the woods yet, given that Isabel might try to lay another egg and the prolapse might repeat, but for now at least, things seem under control and Isabel seems to be doing well.