Advice: Rule One: don't use mods on the SP campaign. They either ruin the fun or blow your install to hell--often both.
However, mods do rule. I've written a few. Great for QB mode.
Strangely, I remember this mission, though it was a few years ago. I was stuck on it for several days before I finally succeeded. And I can't really remember how I did that. Like you, I was until this mission allowing Felix to fly the ship.
Ah, I remember: rule two: Felix is a moron. How he got out of piloting school is beyond me. You need to learn how to fly the ship and fight at the same time if you're going to survive this mission, much less the rest of the game. So switch off the autopilot and take control.
Third: I don't remember if this is the case in this specific mission or not, but I remember that sometimes, BC orders you to do things that either you shouldn't do, or shouldn't do yet, or should have already done. Like, I vaguely remember being ordered to fly to a different planet to chase off the Cardies in this mission, but I seem to recall realizing that, if I just let the Klingons do it, I'd be able to fight the Cardies at Biranu Station for that much longer.
My biggest advice, though, is to play a few dozen quickbattles against (and using) various ships, both strong and weak and in varying numbers, to try to get a sense for combat in BC. Learn how to fly your ship, how to maintain phaser locks, how to fire phasers more efficiently so that you drain all or most of your phaser banks on most every run, how to aim photon torpedoes (a torpedo should never miss in this game, and they should always hit the same shield face on the enemy ship... it will cost you dearly otherwise), and, above all, how to adjust and match speed and heading on the fly so that those enemy vessels can't escape your line of fire.
Once you've learned how to do these things--and it's all practice, my friend--you not only won't have a problem destroying two Galors in two minutes, but you'll have no trouble taking out two Galaxy-class starships with nothing but a Bird of Prey.
That's fun to do, by the way. The trick is riding your BoP along in the Galaxy's blind spot up above the nacelles and pounding its impulse engines into dust. Easily done against one Galaxy, but it gets tricky with two, and you end up having to keep the first vessel between you and the second one so that the second one can't get a good firing solution on you. Also, liberal use of the cloaking device.
Best I've got. Good luck!
As a final word, based on your Flickr photos, you look worrisomely like my tenth grade History teacher. No relation, I hope?