In general, apply materials to groups/components, not individual faces.
In general, leave faces and edges as the Default material so they inherit materials from their groups and components.
This is one of the few instances where materials must be applied directly to faces, and not groups.
See examples: Mapping photo textures to curved surfaces and How to Add a Texture to a Curved Surface in Sketchup
Remove materials with the Material Tools plugin.
Easily replace materials with the Material Replacer plugin.