Alex, I'd like to submit the following suggestions for your consideration. The theme of these ideas is to increase the popularity of certain under-used elements in Starfarer.
Hull Mods
Automated Repair Unit - Also grants a slow in-battle repair rate to armor. Reason: This might well be the most under-used hull mod, probably because there is pretty much always always a better use for the OP cost. A slow regen rate for armor would put this mod back on the map, and give omni-shielded ships without 360 degree shield protection the ability to shield their weak spots while their armor slowly repairs.
Integrated Point Defense AI - Reduce OP cost to same level as Advanced Turret Gyros. Reason: This is truly a nice feature for a hull mod, but it's the kind of thing that you'd want to tack on cheaply if you had a few OP to spare.
Insulated Engine Assembly - Also reduces duration of overloaded effect. Reason: Slightly under-used mod as well, decreasing overloaded duration would give players a genuine selection dilemma between this and other mods at similar OP cost.
Ships (alphabetical order)
Apogee - Convert some existing weapon mounts into universal or add universal mounts. Reason: As an exploratory vessel, the Apogee should be more flexible than other ships of its class. This would also solve the current issue that the Aurora dominates the Apogee in almost every way. (i.e. no need to make Apogee more powerful, just emphasize its flexibility)
Astral - Convert 2 small missile mounts into 2 medium missile mounts. Slightly increase OP. Reason: The Astral is slightly underwhelming for its fleet cost. Carriers should be all about projection of long-range power. Having 2 medium and 2 large missile slots would allow the Astral to generate enough long-range threat to warrant the player having to do something about the Astral rather than ignoring it until everything else is disabled.
Conquest - Increase firing arcs of medium and large ballistic mounts to 175 degrees. Reason: Piloting a Conquest is already penalizing in the sense that you only have access to 50% of your firepower at any given moment. As long as the firing arcs are below 180, the Conquest cannot fire all weapons frontally, and 175 degree arcs would allow the pilot to fire continuously between left and right "wings" of the ship when rotating.
Falcon - Increase OP to 110, increase combat speed to 85, reduce fleet cost to 11. Reason: It's hard to justify use of the Falcon once you have access to the Eagle, unless the Falcon presents itself in a totally different way. Just like the Hyperion might be considered a cruiser-strength frigate, we can make the Falcon a destroyer-cruiser hybrid. If you consider the Falcon with these new stats, it starts to feel like a genuine alternative, rather than a gimped Eagle.
Odyssey - Increase the firing arc of the back-most large energy mount to 360 (or close to 360). Also increase flux capacity to 17500. Reason: With its lower shield efficiency and lack of 360 degree shield coverage, the Odyssey is easily overwhelmed by missile spam. The 360 firing arc on one large energy mount allows for a Guardian PD to protect both sides of the ship, allowing for the other two mounts to serve their respective asymmetric functions.
Vigilance - Add 5 OP. Reason: Gives the player a bit more flexibility in customizing the ship.