This isn’t super easy, I tried a long time ago but gave up. What you would need is a copy transforms constraint that doesn’t actually copy the transforms right away (keeps original rest pose transforms) but instead copies any delta movement. The child of constraint kind of does this but it doesn’t really work with bone chains.
At least now in 4.16 you can export retargeted animations back to Blender using the create animation - preview mesh option, then constrain the control rig to that rig and bake that animation. Then you can edit those animations like any other animation. It should be possible to write some script to automate this, I might do this later if I find some free time.