[Salik Syed]

This might be a dumb idea, but what if you used a PID algorithm.
Use small extremely small values for P, I , D. Set your input (target) to be the joystick, the feedback/output would be the actual PWM. If the constants are small enough you should experience the same effects that you want. If the joystick is held in one place for a long time, the integral term will build up to the PWM value. You could actually change the D term to a negative value so that if the joystick is moved quickly it will have a smaller effect on changing the output.

I think this approach is better than a simple re-distribution of the joystick output, because it takes into account the dynamics of the joystick movement in many dimensions (Positon of the joystick, time it was held there, how quickly it was moved there).

This code should be extremely easy to implement, simply modify some existing PID code to fit these parameters
You will need to tweak it significantly to get it working perfect though.