jmcrook, I know you have tried almost every possible thing but have you considered maybe it is a ventilation issue? These are animals that are very active and have a high metabolism which require more air than say a ball. Does she normally push where there might be airflow? If you catch her pushing how does she react when you open the door? Like will she just lay there for a few minutes with her head on the litter dam?

I know my little guy will be poking around the perimeter of the door where there is fresh air. If I open the door he will just lay there for a few minutes with his head up on the dam before he comes out exploring.

Maybe its a cycle. She gets fed and goes into a food coma for a few days. When she comes out of the food coma she gets active which depletes the concentration of O2 in the tank. That causes her to push at the door to try to get out. To stop the pushing she gets fed, and the cycle starts all over again.