Here’s a method that may work for you.
Above your terrain, create a single plane of geometry, the same size or a bit larger than the terrain.
Paint the plane with the texture.
Edit the texture transparency so you can see through it to the terrain below.
Set the camera in Top View and Parallel Projection.
Position the texture in relation to the terrain as needed.
Position Texture Tool — SketchUp Help
When the texture is in the proper position, right context click on the face > Texture > Projected
Turn off hidden geometry.
Smooth the terrain if necessary. It must be a Surface … Not individual Faces.
Soften Edges Dialog Box— SketchUp Help
Open the terrain group for editing.
Note your texture on the plane above is grayed out when you open the terrain group for editing.
No worries … the texture is still there.
Sample the projected texture with the Paint Bucket + Alt
Click the paint Bucket tool on the surface of the terrain.
Close the terrain group.
Done.