[Geezer (OP)]

A bit later:

I think it should work. I did some experiments with the laser on the miter saw. When I place a square piece of steel on its table and position it so that the laser is just "kissing" the vertical surface of the steel, the laser highlights the raised irregularities on the surface of the steel and they appear as random points of light.

As I rotate the steel relative to the plane of the laser, the points of light become increasingly uniform over the area of the steel surface. At maximum uniformity, I'm pretty sure the surface is plane with the laser. The adjustments I am making are tiny.
The resolution of this method is probably a function of the surface irregularity of the steel. To get the highest resolution I think it should be possible to inscribe a grid on a polished flat steel surface so that only the grid is illuminated as the surface touches the plane of the laser.