UTR, the trick to flyin' the transports is to switch the Cannons to "Gunner AI" during a dogfight. First, you wanna "Target Nearest Starfighter" ("R") and then quickly switch to "Gunner AI" ("F") and fly evasively. Let the "Gunner AI" do all the work. Also, configure your power settings so that your Engines get maximum output by adjusting your "Cannon Recharge Rate" ("F9") to minimum (this doesn't effect the "Gunner AI"), but keep your "Shield Recharge Rate" ("F10") at normal ("Maintenance") to keep your Shields up. Remember to throttle down to ~1/3 to get the best turn rate possible as throttle settings directly affect your turn rate, but don't forget to throttle back up when your not flyin' evasively. Remember, you need to repeat the sequence for each target, so once your current target is destroyed tap "R" and "F" for every target 'til they're all destroyed or until you've accomplished your mission goals. Rinse and repeat.
I'll try to get a video up that demonstrates the above so you can see it in action...
"You know what the chain of command is? It's the chain I go get and beat you with 'til ya understand who's in ruttin' command here."
- Jayne Cobb, "Firefly"