How do I create prefab variants for different 'Heroes' in my shooter?

I have a base prefab that holds all the important, generic info for each character (Dying, movement, character controller etc.) That base prefab has an existing character mesh and bone set-up. How do I replace the mesh for each prefab variant with a new character mesh I have?

What I tried was deleting the old character mesh and then adding in the new character mesh. Then I changed the 'Root Bone' in the Skinned Mesh Renderer. This makes the character mesh correct but he just T poses the whole time.

Here is the structure

CharacterBase
  - AnimatorAndRig
     - HeadMesh
     - Body Mesh
     - root
        - pelvis
            - spine (etc)

I then get a character that has the inner structure

NewCharacterAnimator
   - HeadMesh
   - Body Mesh
   - root
     - pelvis
        - spine (etc)

I then replace the Mesh parts with the new prefab mesh, assign the Root Bone to the correct bones on the existing root on the CharacterBase.

Is it the avatar that's the problem? Is the current avatar not mapped to the new character mesh or something?

Sorry this might not be the best way to do this but I really need help If I'm going to try to create 10+ heroes. I need to get this right.

Thanks