As a sci captain on my most played character I run a Battlecruiser.. mostly for the surivability with my Sci captain providing a boost to damage out put through the use of photonic fleet for PvE play, with consoles tossed in to boost emitter effects.. (The character build is specificly set up to boost this)
Someday we will get a Klingon science ship.
While I really don't have any specific suggestions I can say that you should take "Holoistic" approch to what ever you decide to do. Right off hand I don't recall what the BOFF slots on the mirror Qin. But start with your character first.
On my own consistant I wanted to have a consistant damage dealer with the player powers enhancing that ability. I next looked at the math and numbers. I wanted to deal consistant deal damage over time that was less bursty. I specificly did not put any skill points into torpedo weapons on this character. My Battlecruiser is an all cannon build with dual heavy forward that are specificly fleet weapons with [Acc] [Dmg]x3 disruptors, and the same for the 4 turret in the aft slots. KDF Battlecruisers have the manuverability to get those forward cannon on target, but in my own play I found most torps usually wasted themselves against shields. ('pengs being the acception because of that lovely DOT.. and I can always slot one of those in.. but that slow rate of fire *sigh*)
So I personally try to keep the ship and character as a specific unit with each complimenting each other with powers and abilities. I cant think of anything I else I can think to add..
Cryptic... Perhaps THE most single most aptly named game studio ever to exist. Especially when it comes to STO.
I run the mirror qin and love it (granted it's on my eng, so survivability is a little higher).
I run mine with a simple "escort" set-up... DHCs and a quantum torp up front with turrets in the rear.
I would suggest something similar, with full spec into flow capacitors and a polaron build. You should get some good spike damage and a good amount of drain, if built correctly.
I would suggest looking at STOAcademy's build page for some ideas but I imagine that a subnuked and drained enemy is going to go boom fairly quickly and if not, will only tickle you slowly in response to your barrage.