Retargeting raw bone transformations with avatar definition onto a different Avatar + hierarchy

The goal is to retarget the animation from a dynamically animated character onto another whose correspondence is encoded in Mecanim.

The problem boils down to: How can I bake a character's instantaneous bone transformations into muscle values? I change the bones' rotations in code in real time, there is no underlying animation clip. If you don't understand this significance of this, consider the following code: What goes into the TODO?

Source Character:

 void Update() {
    // ... Some process which sets the rotations on each of the character's bones.
 }

Destination Character:

 public class Retargeter : MonoBehaviour
 {
     public Avatar sourceAvatar;
     public Transform sourceRootTransform;
     public Avatar destinationAvatar;
     public Transform destinationRootTransform;
     private HumanPoseHandler sourceHandler;
     private HumanPoseHandler destinationHandler;
     private HumanPose humanPose;
 
     // Use this for initialization
     void Start()
     {
         humanPose = new HumanPose();
         sourceHandler = new HumanPoseHandler(sourceAvatar, sourceRootTransform);
         destinationHandler = new HumanPoseHandler(destinationAvatar, destinationRootTransform);
     }
 
     // Update is called once per frame
     void LateUpdate()
     {
         // TODO: "Bake" the source character's bones into the muscles 
         sourceHandler.GetHumanPose(ref humanPose);
         destinationHandler.SetHumanPose(ref humanPose);
     }
 }

Both characters have avatars, and this code works fine when the source character's animation is being driven by an AnimationController and a regular animation clip. It stops working if some process is setting the bones manually. I understand that there has to be some process which turns these bone transformations into muscles. Does that process exist?