The problem is there is always green poop on the area (circled in purple), which is a considerable distance from the vent (circled in orange). I am now convinced that the poop is coming out of that area and not her vent.
She is eating, not a lot, but more than I had expected of a gruel of chick starter, molasses and a dab of olive oil. Very thin.
You can see in the second pic that the area circled in purple is raised up. It looks to me like her vent has atrophied. I've been treating her for a month now. I don't want her to suffer and I think I'm heading toward euthanizing her.
I'm so sorry that she is not getting well.
I do see the area that is raised (purple circle), do you see waste coming from that area or are you finding it there? Since it's raised, is it possible that the poop is just getting stuck there? The only thing I can think of would be try diapering her, have the diaper above that raised area and only covering the vent and see if waste comes from there or if you find waste in the diaper that is covering the vent.
May I ask about the Molasses? I'm not criticizing at all, I think you have done a remarkable job taking care of her! I know that Molasses do have health benefits, but they also act as a laxative in chickens - very common usage is for constipation and even as a flush for toxins. Oil would also act as a laxative.
Have you tried enticing her with some egg (scrambled/hard boiled), beef liver or fish (tuna, sardines, mackerel)?
I'm sure this must be so heartbreaking for you. If you do make the decision to put her down and can't find someone to help you, the lab at K-State will probably do that for you. Most labs do accept live animals and put them down (there's a fee I'm sure), that might be something to ask about.
Just some ideas. If your interested in experimenting with a diaper to see if the waste is coming from that section, here's an easy and relatively cheap way to diaper a chicken. Quite a few folks have done this.