Aiming issues with the cannons? A slightly wrong angle resutls in just the turrets firing....
Fairly sure this is the case. If you aren't careful, this can happen easily enough. fly with arrays on the aft section, to get yourself used to firing with just the DHCs. The turrets on the back might be fooling you visually into thinking you may be firing with all weapons.
I'm gonna agree the issue is your firing arc. Beam arrays have a wider arc so you're firing at your target more often than you are with DHCs. DHCs have the narrowest arc of any weapon (IIRC) certainly much more narrow than a beam array, or even dual beam bank.
Your problem isn't your loadout, it's your flying. You need to practice turning, sprinting and keeping your ship's bow pointed directly at your target.
In an escort spec'd for cannons, with 3 DHC and turrets you should be shredder.
Remember what fighter jocks say, "One Pass- Haul ...." In an escort you don't have the hull and shields for a turn fight.