You’ve got it pretty much figured out by your own reasoning good sir.
You’ve also gotten a log of good advice.
My first recommendation is to get the Dominix Navy Issue - more everything and easier to fit lazily for L4.
Second use the ships bonuses as you’ve no doubt read a dozen times over by now. Sentries and Hybrids. While certainly she can get right in the nitty gritty there are better ships for that style of play, yet this is a versatile ship and can do a lot. Even out your skills more so for this ship if they are not already there. MJD is a must for sniping and the Warden II give you the best range.
Here is my generic fit. With a mission fit I opt to use named large hybrids and factional ammo. I can swap my LPs on the cheap and I prefer anti and thorium for range specifics. You can certainly swap the bling armor repairer for a TII - but running a set of Askelpians I don’t need much of a tank.
I did add the faction rat specific hardeners, or you can always use an EANM and 1 hardener for your specific mission. I carry a mobile depot to refit on the fly and the mods I carry in the hanger speak for themselves as to why they are with me. This is a cap stable fit for me and by changing the hardeners I can park her fat butt on any mission and go take a nap if I wanted. Also with a fit like this I can pop every frig, destroyer, cruiser, battlecruisers and a lot of the BS at range and before my shield even changes color on most missions.
[Dominix Navy Issue, [PDTS]]
Drone Damage Amplifier II
Drone Damage Amplifier II
Drone Damage Amplifier II
Magnetic Field Stabilizer II
Federation Navy Armor Kinetic Hardener
Federation Navy Armor Thermal Hardener
Corpus A-Type Large Armor Repairer
Large Micro Jump Drive
Cap Recharger II
Cap Recharger II
Federation Navy Omnidirectional Tracking Link
Federation Navy Omnidirectional Tracking Link
Target Painter II
425mm Prototype Gauss Gun
Drone Link Augmentor II
425mm Prototype Gauss Gun
Drone Link Augmentor II
425mm Prototype Gauss Gun
425mm Prototype Gauss Gun
Large Capacitor Control Circuit II
Large Capacitor Control Circuit II
Large Auxiliary Nano Pump I
Warrior II x10
Warden II x5
Vespa II x10
Ogre II x5
Federation Navy Antimatter Charge L x1500
Scan Resolution Script x1
Nanite Repair Paste x200
Federation Navy Thorium Charge L x1500
Targeting Range Script x1
Damage Control II x1
Sensor Booster II x1
Shadow Serpentis 500MN Microwarpdrive x1
Capacitor Power Relay II x1
Corpum C-Type Energized Adaptive Nano Membrane x1
Magnetic Field Stabilizer II x2
Large Ancillary Armor Repairer x1
Drone Damage Amplifier II x1
Cheers