I'm not sure if you're aware but beams actually deal only soft flux to enemies, so they will be able to dissipate all flux you deal without dropping shields. Other weapons like kinetics/blasters deal hard flux which will not dissipate unless the enemy drops shields or vents. Your only hard flux is the HVD, which probably works well enough because the paragon is so strong, but as Goumindong said, 4x HIL is mad overkill, you really don't want to be shooting HIL into shields, it's flux inefficient and only dealing soft flux and 2x HIL is more than enough anti armor damage for anything in the game. 2x auto pulse would go a long way if you have no tach lance.
The reason tach lance is so good is that it is a big burst of damage so the soft flux doesn't matter since the burst will still overload or force enemies to drop shields. I usually use 4x tach lance paragon, which is enough burst damage to one shot most destroyers and all frigates, it's super strong. I actually consider paragon better at killing frigates than any other capital because it has insane (2000) range and can one shot frigates, so you just have to wait for them to wander into range for a free kill. It's much easier and less risky than any other method of killing frigates besides fighters.
Also with regards to the conquest, pretty much any ship properly flown by the player and in the same class as the enemy will beat the AI. For instance, it is possible for the player to consistently kill a paragon with any other capital in a 1v1 but that doesn't mean the Paragon is not the best capital. A properly outfitted and player piloted Astral will also always kill an AI conquest. Astral doesn't even really care about the missile slots, it's all about the fighters. I know some people even leave the missile slots empty to have more OP for strong fighters and supporting hull mods. You should definitely not put your most aggressive officer in a carrier, you want carriers to hide way in the back, since they massively outrange everything with their fighters. Aggressiveness corresponds to positioning more than 'firing weapons' a cautions officer in a carrier will still attack things, he will just hang back which is much safer. There is no reason for a carrier to intentionally go into enemy weapon range.