NavList:

The solution offered has some issues which need to be resolved. 

The presentation of the laser to the sextant is important.  If we intend to stuff the beam through the telescope, then it must be coaxial to the telescope ' centerline.  Off center or at some angle to the telescopes axis won't do.  If we intend to just cast the beam directly at the index mirror, the beam must be parallel to the plane of the arc AND simultaneously intersect the axis of rotation of the index mirror.  It won't do to have the beam walking across the index mirror as it is rotated.

The laser dot on the wall isn't some infinitesimal small crisp circle.  On closer inspection, after a throw of 30m, you will find that the dot has an appreciable size and has scintillating fuzzy edges.  Go try this for yourself. 

The distance to the wall has to be precisely known, from the reflecting surface of the index mirror, from the "point" of reflection.  

So the two most critical dimensions (rise and run) will likely be imprecise.  That is going to cause some unease with the precision of the trig.

When the index arm is set to zero, the beam of light must be precisely  perpendicular to the wall.  Otherwise the trigonometry is more slightly more complicated, as you must then know the starting and ending angles.  Instead of a right triangle your trig solution requires, we have an oblique triangle.

The solution isn't traceable to NIST.  I know most folks trying to calibrate their sextant's arc won't care about this, but for industry, this complaint is fatal.

Brad