A flat back floor is a whole lot noisier than one with a spare wheel well punched into it. My work car has the flat floor and spare underneath, it was like a drum. It took a decent layer of foam and a wooden rack bolted down to stop it drumming and shut it up.
Cutting stuff out underneath isn't going to help your back window stay clean. All hatches and wagons have that issue. You could fit a roof-top spoiler to divert air down in the back, but it would create lift at higher speeds. Little bit scary.