A possible solution is to rotate the assembly frame 90 degrees to have the longer side of the frame along the Y direction rather than along the X direction. In this configuration there would be about 33 cm between the larger outer frame and the assembly frame, enough space for a person to stand.

In this configuration the back of the mirror would face the +X direction and we would require an extension of the clean booth in order to put an oplev, which we'll need in order to align the mirror when hanging. See the attached drawing.