With all respect: If you start with the mirror principle it means that leaving one universe at one point of the membrane makes you enter the very same universe at the very same point, for the closest point to that mirror from the other side is the very last point you left on your original side and not the opposite end of the finite room.
If it was, you could whitness crossing the border of your finite room thus could not experience endlessness. Endlessness is only there if you cannot realize that you cross an invisible membrane. That is why your explanation with boxes, (which is easy and cool to follow) at one point needs entangled spheres. Any “border crossing” involves a 180° turn to face the same mirror in the same angle.
In that sense our world could be nothing more than a reflection of ourselves in a mirror.