Overriding Idle Animation with IK

I am trying to stabilize the hands of a character during idle/run animations. This is a true first-person perspective and I don’t want the gun bouncing all over the screen. I’ve tried using FABRIK IK to solve this issue, but it seems that once the hand is moved to the effector location, the idle animation kicks back in and will drift the hand around the effector location. I want the hand to stay locked to the effector and not move while playing the idle animations on all the other bones. I have tried blending the bones so that the hand bones don’t play through the idle, but the animation in other bones, like the pelvis, still pass down movement to the hands. I don’t know if I should look towards getting a better idle animation to fit my needs, or if there is a way to prevent the sway I’m still experiencing using IK. Thank you for any input or ideas.