These chickens have never been wormed, so I at first thought that's what the problem was. I thought about dosing the whole flock, but didn't want to unnecessarily stress out their systems. However, I was also afraid to dose Awk singly for fear of giving her too much, so I didn't do anything

I have heard is that too much antibiotics for too long can cause vent gleet (consider the same problem with humans), and though we've never given them any, they did have a previous owner who bought them from the farm supply.
I did some treatment on Awk. About a week ago we tried an Epsom salt flush. I dissolved 1 tsp in 1 ounce of water and gave it to her by syringe (she didn't mind much). She pooped a little runny but the vent gleet was still there. A few days ago she got a serving of oatmeal, yogurt, acidophilus capsule contents, raw garlic, and apple cider vinegar. I also took a syringe and squirted some ACV into her vent (supposed to settle the unbalanced pH that comes with vent gleet). She finally laid again after three days, and if you know red sex links you know that's a long time! Her poops look normal but she's still oozing goopy white stuff from her vent. I'm going to give her another dose this week and then give her a long warm bath. She still has low energy, she's off balance, she preens constantly and gets this far off expression. She's still eating and drinking and dust bathing and laying. Awk ocassionally will start to get her energy back, but then she lays an enormous or weird egg (last month she laid a double yolker, a few soft shells, and a yolkless) and she reverts back to her slow-moving, glossy-eyed, off-balance self. I just feel like the whole situation's a bit hopeless. I guess I'll move on to Monistat in a few weeks if I can't get these other remedies to work, and maybe there's another way to get some Nystatin.
We're moving in August and we have to sell most of our chooks, but I have no idea if someone would buy a girl with a goopy vent, so I'm trying desperately to cure her before then. I'm just running out of ideas...