The music (especially the first two tracks) really conveys the feeling of sands in the sense of sand dunes and such. And while I like the sound of the final track, it feels more like the wild west, and even in a cartoonish style - nothing wrong at all - I quite like it - but it breaks away from the other tracks.
The main menu track could easily work in a puzzle-kind of game setting, a bit like You describe the idea.