I agree. Maybe one of the universities near you can do some testing on your duckling for free. If not, there are other places you can use and send samples to yourself like Avian Biotech or University of Miami. The cost can be quite high though depending on what all you have tested.
Based on all the information, I am leaning towards some sort of obstruction at this point. If it were a significant impaction, she wouldn't have made it a month most likely. If it were something like cocci (which can stunt growth), there would mostly likely by blood in the stool and/or listlessness.
If it were bacterial, she would probably have the swelling all the time, not just when she eats. If it were entirely genetic, I don't know why she would have the swelling just after eating either. Through the process of elimination, I am betting there is an obstruction that is causing air to escape under the skin when she is eating. It may be just enough that she is getting enough nutrition to live, but not to grow.
Could your vet do an x-ray to see if there is something obvious in there? If it is an impaction or obstruction, you can use oil (like Cod liver) and a gavage needle (blunt tip usually curved needle) to try to loosen it with massage. I have done this successfully, but unfortunately lost babies doing it too. If it is something rigid like a screw or something, it would have to be done surgically.
It is just so hard to say what it could be. Really, it could very possibly be a combination of things going on. At any rate, I so hope she pulls through! She obviously is a strong bird to make it this long.
