IK Pinning

I'm trying to maintain the position of a pair of IK hands on a Game Object that has its own Animator.

Example: A character keeping their hands pinned to the horn of a horse saddle.

Currently, I have the left and right IK targets in an empty Game Object which has a Parent Constraint to the nearest bone to the horn of the saddle. I'm experiencing undesirable "floating" of both IK targets, seemingly delayed to the movement of the horse.

I'm using the IKControl sample script from the IK documentation so nothing fancy, just trying to figure out if it's possible to pin the hands in place.