The distances at which shadows are rendered are currently fixed. FSO uses a cascading shadow map render with three shadow maps, with distances of 400, 3000 and 20000 as cutoff points (As in, everything up to 400 units away from the camera gets rendered into the first map, everything up to 3000 in the second and so on).
What we do not want to do is introduce lots of special cases here. I think what would be worthwhile is to introduce commandline switches or mission spec fields to control the shadow cascades.
And yes, shadows on the player ship or cast by the player ship are the most noticeable ones, so they're not gonna go away.