Changing firing arcs would mess with the AI and go against the ship's design. It's the most visually broadside-based ship in the game. Instead, I would simply give it a slightly narrower and harder shield, and slightly thicker armor, to help the AI not flux-lock itself from excessive shielding. The Conquest is completely fine as a player ship - if you can wrap your head around piloting it, it's quite powerful. Two large missiles and the ability to circle targets at max. range is a great asset. The Conquest simply needs to not get surrounded, and it can usually defeat any enemy, save for battles where it's forced to duel other capitals - which it can still do handily in the campaign with player skills. Could also give it Maneuvering Jets with 2 charges, so that you can get to the battle faster or choose to store one emergency charge for evasion.
Regarding not being surrounded, if you're fighting destroyers and frigates, you can actually use both broadsides at the same time to destroy swathes of enemies, which is when the ship feels most satisfying. Too bad it's more optimal to make a 1-sided loadout right now.
It would be complicated, but some sort of built-in hullmod dedicated to encouraging double broadsiding would be pretty cool for the Conquest. Current vanilla variants have abandoned symmetrical loadouts entirely, which I think is sad.