I use the star cruiser with my max level engie. Have 4 polaron beams front, 3 aft plus one tricobolt in back. Got consoles to boost beam weapons.

I always try to keep my ship sideways to the target so all beams are hitting at once. Also I make sure to keep the power level up with EPS power transfer/Nadion etc. I also use the Emergency Power to Weapons I ability which gives me 8% damage boost.

Even with 7 beams and max power I'm still not doing enough damage. Bops and Raptors shields often barely seem to move.

What can I do to boost damage output without sacrificing a ton of defense?

You picked the wrong class to try to DPS with.

Engineer in Star Cruiser is almost entirely stricken to support duties.

Even with broadside beams, I would be able to stay at or near 100% with nothing but 2x EPtS, Engineer Team, and balancing my shields.

To be openly blunt... no, there isn't a way to do any sort of meaningful damage with a Star Cruiser. Even Beam Overload will only affect 1 of your many beams and won't be enough by itself to actually do anything even if your enemy does get careless/stupid enough to actually let one of their facing shields slowly widdle away.

Yeah I rolled the engie to focus on support so I knew I was going to lose alot of DPS. Just wanted to make sure I wasn't missing any tricks in my attempt to squeeze all the firepower I could out of my ship.

Why not just go healbot build or switch to an Assault Cruiser if you want some sort of hybrid.

When I've looked at using other ships it always seems I'm giving up more than I'm getting in return.

If you want to do damage with a cruiser get a Dreadnought.