Key flaw in the Conquest as a Battlecruiser is that it's attacks going broadside are belied by a weaker structure poorly covered by it's shield. While other capitals go full frontal in guns, armour and shield,
The Conquest has to split it's fire, so the maximum amount of its firepower it can be built with will not be realised without flipping the ship 180 degrees, which isn't very viable in a slugging match as you expose the ships vulnerable sections in that turn.
The key problem however is that it's flux effeciency is still a Cruiser with the guns of a Capital. Which means it simply can't last an engagement, and it's speed is hampered by the fact that flux drops speed at all.
So
1. Increae the flux cap and dissipation in line with actual battleships
2. Increase impulse speed and base maneuveribility/make the ability jets recharge a lot faster.
3. Allow the main guns to have greater turning radius
Ultimate: Revert to 0.32a Conquest, all 3 Heavy Ballistic slots on each "wing"