I can tell that the toes on one foot are curled so isn't that a good sign of vitamin deficiency and not the dreaded Mareks?
In my experience... the toes curl automatically when the leg is retracted to a certain position... it SEEMS like.
Marek's does stink, but having a good understanding makes it not as dreaded. It doesn't have to be a death sentence for a whole flock.
The mouth discharge would indicate to me that it isn't vitamin deficit. Gasping is not a good thing and to me an indicator of decline.
I would not put egg on the beak. I would just make food available. I don't think a vitamin deficit would stop them from eating.
I understand the desire to save the life of this bird... but sometimes we MUST do what is in the best interest of our whole flock. Taking in a failing bird is definitely not going to help your birds. I have a feeling the owner was making the right choice... a difficult choice, but sometimes necessary. One life or many? Sorry, I don't mean to harp on you... and I hope you will have no regrets, but also that you might consider your flock more seriously next time. (I know it was from next door, but that still isn't QUITE the same to me). Even if it is a vitamin deficit... all the other birds in her flock doing fine mean this one would have a genetic issue... inviting weakness and disease to take her down first or to live among the flock. Death... keeps a flock strong, IMHO.
With development of new symptoms, I would cull and send the body for necropsy tomorrow.
Here is a symptom checker tool you can see if you can narrow something down...
http://www.poultrydvm.com/views/symptoms.php
As the other poster said it could take several weeks of treating with vitamins to see recovery. Whatever is right for you, even if I disagree..
Have you seen these chicken slings to help get weight off their legs and stretch? The muscles in the legs are just going to atrophy (waste) without any use... so I think you need to do some physical therapy otherwise, it may be too much weakness to notice the improvement when it starts to take place. The muscles get tight and shortened from being in the same position and becomes uncomfortable to move them even more... speaking from experience of a dislocation that was on a splint/sling for 6 weeks... and still recovering a year later....