Binding works beautifully, but there is an issue with baking:
If I follow the new instructions (select the rig only, not the rig and the movement armature), then the resulting baked animation has very wild deformations.
However, this doesn't happen if I follow the old way of selecting both the rig and the armature, then clicking on a bone from the armature before proceeding to animation -bae (all other settings are exactly the same).