This was why I liked APB. It was to FPSes like Team Fortress 2 what Enemy At The Gates is to Rambo. The pace of combat was nowhere near as frenetic, and it required more tactics than reflexes; if you could outthink your opponent, you could negate their twitch skills, and there were vanishingly few circumstances where there was only one solution to a problem.
You should be using only a very few buttons; most of the control is from the mouse. And a trackball is nothing like a mouse.
Personally, what I find helps is to shoot enemies in midair, when they have little or no control over their motion. I pre-position the crosshairs at a point where they will be, and then shoot when they get there, so it becomes a matter of timing, not aim. This probably isn’t as viable in the more realistic games, though, without longjump ramps and bounce pads.