The scheme referred to here was to make the ICBM as shiny as possible and spin the upper sections so as to spread the heat of the laser as much as possible.
Another possible countermeasure is to release a metallic cloud or fog from the nose of the missile so as to reflect as much of the beam as possible.
I know that, but it is easy enough to go back to spinning, if desired. At what point in the boost cycle it would be best to impart the spin is an engineering problem. I would guess that the easiest would be to put on the "spin" just at the end of the boost phase, when the warhead "goes ballistic".