I was afraid of this. I know about everything you just mentioned but I was hoping I had missed some little-known shortcut. I guess not.
It's not a simple planar surface. I had to manually (and very carefully) get the current bounding box size of the object, then I scaled it, and then I re-positioned it very carefully...
In this case I was making a ship (boat) hull. I had to reposition the smaller inner hull piece in the center of the larger outer hull piece.
- First, I got the bounding box.
- Second, I drew a line from one side of the top-midpoint of the hull piece to the other side.
- Third, I hid the skin of the piece.
- Fourth, I copied the piece. Then, I calculated the smaller piece sizes and scaled/stretched each side appropriately.
- Fifth, using the midpoints of the line I drew, I re-positioned the smaller piece in the middle of the larger piece.
- Sixth, I deleted the lines and un-hide the skins.
It's a lot of work for something that should have been in the basic Sketchup interface to begin with...