Less strafing, more aiming
Most online shooters have similar issues, where players move left to right non-stop to avoid getting shot, whether they're being attacked or not. I also do it, because there is nothing which penalizes me from doing it. I've played both casual and realistic shooters and something that I've realized is that gameplay is far better when strafing penalizes you. My suggestion is that when moving around, your cross-hair starts to wave around until you stop moving. The player which stands still and is aiming, should always have the advantage.
Think of it as a recoil for moving around. You should be able to still do it, but you will be slightly penalized for doing it. Perhaps weapons which are larger, could have a more severe recoil for moving while shooting. That way, more agile players will want smaller guns, which may not be powerful, but allow you to dodge while in a gunfight.
