but I think plopping some terrain features down on the surface (and/or hills underneath) would create a usable surface?
It does! I've got a couple of 1"-2" slabs of Styrofoam cut into hill shapes and stick them under (or on top) of the battlefield blanket. If you look in the background of the photos, I also have an O scale train layout. The trees are on bases and I frequently place them on the battlefield when gaming WW2. Convenient because I don't have to store them in boxes when I'm done with gaming, I simply put them back on the layout.
I think the Cigar Box battlefield is washable, need to check on that.