TL/DR: Boost power to the damaged engine
So I was flying in a fury today. In a fight one of my engines was damaged slightly (93% health left) and everytime I gave some forward thrust, the ship would turn slightly.
I figured I'd mess around with the engines to see if I could try to compensate for the damage.
Going into the Power MFD (middle mouse click to lock zoom so that it doesn't affect scrolling) then overpowering the damaged engine slightly made it so that I no longer turned everytime I gave it some forward thrust. It was a pretty big difference and made the ship flyable again.
Additionally, there's probably the option of underpowering all of the other engines in the case of a severely damaged engine, but I figure this tip is enough to help anyone that gets caught in a bind.
Thanks for the tip, will definitely be trying this, especially the middle mouse click lol