I see lots of people imagining one another to be at different points on a mental model, and I don't deny that people behave that way, but to me, that doesn't mean the mental model is at all accurate to reality.

I don't think what you're saying here makes sense. The "status model" only makes claims about people's behavior. If people behave as though status were a thing, that makes status a thing.

By way of analogy, beauty is also imaginary in the sense that status is imaginary. Lots of people imagine each other to be at different points on the beauty scale, and act accordingly, but there's nothing objective out there corresponding to beauty. Sure, there's things that lots of people would agree are beautiful -- symmetric faces, lack of disfiguring scars, whatever -- but these are arbitrary -- there's nothing intrinsically beautiful about them. (Similarly, wearing a gold watch or whatever might be a sign of status, and is also arbitrary.)

Would you say that you "don't believe in beauty" in the same way that you "don't believe in status"? If not, what are the relevant differences?