Animation Montage based on animation sequence overwritten by older animation sequence

Currently, I have an animation sequence that I created by duplicating the ThirdPersonIdle animation from the third person game template, then editing the duplicate into a punching animation. That sequence, called PunchAnimation, seems to work fine.

However, when I create an animation montage based on PunchAnimation, the bone motion from PunchAnimation only plays on bones that had no motion in ThirdPersonIdle, and bones that were used in ThirdPersonIdle follow the idle animation instead of the punching one. This results in the character performing the idle animation everywhere except the fingers, which still close into a fist as they do in PunchAnimation.

So, essentially, how can I stop PunchAnimation from being overwritten by ThirdPersonIdle (which it was based on) in its animation montage?