Night and day absolutely could work, the only reason you think it won't is because you are starting from the assumption that the sun is a ball of fire. If it's a spinning spotlight than night and day would behave similar to how it does now. And I don't understand why you think it would be a universe between us and China? The dimensions are clearly marked as equal to what we have measured the earth to be.

However there is a flaw. If the heavens are as small as illustrated then we should be able to look up with a telescope and see the other side of the earth.

For this to work there would need to be a black hemisphere, starting roughly near the firmament.

This is very easy to test though. Assuming gravity in this scenario is a result of the centripetal force of the rotating earth, we would expect gravity to be more powerful at the equator and diminish towards the poles. You can measure gravity pretty easily by making a video recording a falling object. A high speed camera would work better but isn't absolutely necessary. For the object I would use a lead ball and conduct the experiment on a calm day.

Alternatively you could try hitting the firmament with a rocket or a weather baloon.

Anyway. I think it's bullshit too. But your reasons are pretty weaksauce.