Not entirely sure what you mean by " I am trying to model the reflected projector instead of a projector and the mirror".
The way I see it the mirror acts like a virtual projector behind it. The angle between the actual projector and virtual projector is 2x the angle of the mirror in both X and Y. The image will be upside down and the center of rotation for the virtual projector is the center of the mirror.
Here is my crude drawing. Does this help in any way?
I didnt even know those mirrors exists, but they look awesome! Imagine combining it with something like this: https://lightform.com.