yeah UV mapping is what works
you don't really need to make things smooth
I haven't done any smoothing on any of my models. The reason you don't is because smoothing makes more faces, which in turn will make the FPS on the game go down.
Let me show you an example I made real quick.
My basic model was the same as yours, then i went into edit mode, and front view and selected all of the top vertices of the coffin
Then, I extruded up a little, then scale it in, so that it made an incline in, which shaped the top of the coffin.
Next, I moved the bottom up where it was small, so I could get that line that runs all the way around, then extruded it down to make the bottom walls of the coffin.
Then I selected all of the faces except for the very top part of the lid, and UV textured them as squares.
Finally, I selected all of the top parts of the coffin, UV unwrapped them from the top view (projected from view), and stretched the map out to fit the whole square of the texture.