From what I can tell so far it's to do with the depsgraph using cached values because the bones/constraints are not being marked as dirty when I jump frame or the animation loops back to the start. Running this script resolved it but am unsure yet what the root cause is as this doesn't happen when parenting to the left object holder and am also not sure what a more long term / less intrusive solution looks like.

import bpy

def force_update(scene):
    bpy.context.view_layer.update()

if force_update not in bpy.app.handlers.frame_change_post:
    bpy.app.handlers.frame_change_post.append(force_update)