If a heavy battleship has pulses and cerbs, it will not be able to damage the light when the light's shield is down due to range. 1 mortar would be too few, but if it had 2, it would be vulnerable to a charging medium battleship with cerbs (or even light if the player knows the heavy's blindspots). A heavy battleship should win against any other from point blank range, but in this case that would not be possible.
On the other hand, if the heavy battleship had an ionblast, prims and a mortar, it would be able to take out the light, but in that case your idea about reducing prim shield damage would have no effect whatsoever. I agree with your idea about the Ionblast, but depriving heavy battleships of prims would nerf them even further, after the cerb nerf.