The biggest problem is your mindset as you've already admitted. The Star Cruiser is nowhere near the top of the list on damage dealing Cruiser preferences. She is a healer and a tank above anything else and while you can squeeze some damage out of her, you'd be better off running it as a healer to support your team.
The SC has a very low turn rate, making DBB's and Torpedoes weak weapons overall as you're constantly trying to bring your respective arc's to bear on the target rather than focusing on the well being of your team and unleashing a 6-8 beam broadside at full weapons power without much turning work. Only Engineer's can get away with a full 8 beams effectively with EPS and Nadion Inversion cycling, while the other classes stick to 6 beam and 2 torp or mine launchers. Don't even think about using turn rate consoles either as they give a percentage based increase of the normal turn rate which I've already pointed out is abysmal. Example: +10% turn rate of a base 9 degree per second yields only 9.9 degree total, whoopdeedoo! That slot is better utilized with other consoles.
Onto abilities -
FAW is ok for clearing spam or whittling away a single target, but with multiple ships it's not that great. I use it in my dps build while I keep AP: Delta in my healing build (or a second Tac Team). Speaking of which, Tac Team is a must and finds a home in the Ensign slot of every ship I have. It's invaluable at clearing tac officer debuffs and distributing shields rapidly to compensate for heavy damage (works much faster than the standard distribute).
Engineering...
Again, this depends on your mindset. I keep mostly heal and support abilities here, though I do carry a DEM + Warp Plasma combo for s***s and giggles. With your power settings either at full weapons or full auxiliary and the rest in the non primary setting your shields and engines should end up in the mid 60's which is plenty for a Star Cruiser seeing as you're not trying to be quick on your feet and by cycling EMPTS abilities you can cap or come close to cap'ing your shield power almost 100% of the time.
So I run -
ET 3 (third in my hull heal preferences, to keep my other teams up more often in case of emergency)
ET 1 (clearing critical debuffs, normally TSS shields or Viral Matrix)
2x Extend Shields 1 (support, keep Extends up full time unless shockwaved)
EMPTS 3 (tanking + prebuff before using ES)
EMPTS 1 (minor damage + prebuff before using ES)
Aux to SIF 3 (first in my hull heal preferences, fired around 80%, excellent hull resist and quick recharge)
For my SCIENCE -
TSS 1 (most shield resists here, the heal is weak, but together with ES it can blunt a significant amount of damage)
HE 2 (second in my hull heal preferences, normally fired around 65%, good hull resist especially on top of SIF 3 or AP Delta or ENG Fleet)
ST 1 (due to the prevalence of SNB's, Scrambles etc... You're going to use this often)
* Polarize Hull is mostly a waste with the wide array of ENG hull resist buffs and the fact that a SC has the raw power and inertia to escape Tractor Beam's with full engine power and/or evasive as well as being able to power right out of a Gravity Well. Tractor Beam? Meh, I leave that to my supporting Science ships. Feedback pulse... Version 1 isn't very powerful and needs to be full Aux to do any damage, which takes away from your Weapon power (unless battery or EPS).
* EMPTA 3 is simply a waste too. With 125 weapons, 65 shield/engine and 83 Aux it's overkill on a SC.
I swap consoles around from time to time, but generally I run:
Full Borg Set (occasionally resilients shields for spike damage teams, otherwise regen's for shield strippers and low dps crews).
Neutronium Armor (more than 1 is overkill with Eng buffs), Shield Cap, (Shield Regen + SIF Generator or 2 Plasma Manifolds).
Induction Stab, Halon Console and Borg or Crew Recovery (testing effectiveness atm).
2 Phaser Relays (or 1 + Borg)
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Well, good luck with the SC. And there are a bunch of us out there, we're just normally tied up with supporting our fleets, not hanging around space dock
