I wish I could figure the minimum set of preconditions to get this.

1. In blender, assign materials to the faces to be textured but do not define textures.
2. Still in blender, assign a material to all remaining faces, so no faces are left "naked".
3. Export the object, import it as furniture in SH3D
4. Apply the material properties in SH3D. You'll find all blender-assigned material names assigned to the respective face groups and can texture them here.[/list=1]This way, the textures are not distorted, and true to scale.
   
   But
   Request for advice: How to align a texture with the textured faces? See *.sh3d and *.pngs:
   1. How is the placement of the texture's origin determined/controlled? Mathematically, it maps to the cross on the red diagonal extension. No face, vertex, object, nor bounding box corner there. Offsets x=y=0%, angle=0°, scaling=100%.
   2. How to avoid the vertical offset when mapping the same texture to two parallel faces? Vertical view angle perpendicular to the face. The rear mapping (green "shadow" as the green is transparent) has an actual vertical offset to the front one. It's not a perspective effect like the horizontal offset.
      [/list=1]Have I missed something or are there workarounds?