The constellation is subdivided into orbital planes, with ~20 to ~60 satellites in each plane chasing each other around the planet.

The following is somewhat speculative:

The bearing to the next satellite ahead or behind you in the same plane should be roughly constant; likewise, the bearing to satellites in adjacent planes orbiting in the same direction will change slowly during most of the orbit.

Near the poles the required slew rate will likely be too high to keep the side-to-side links working but that's also a part of the planet where subscriber density will be low so losing that capacity for periods of a few minutes when near the poles likely won't matter.

Does the laser pointer have azimuth and elevation as free parameters like ground receiving antennas?