I think you design is quite nice. I have a suggestion though. What if you simply put context sensitive buttons on the search results themselves. For example, if you search 'Mike', the contact result would display a Phone/Message icon; if you search for a song, it would display a Play/Pause button. I feel this approach can reduce the number of steps even more since you won't have to select the filter at the bottom. What do you think?
This is great work! I could see a form of this being pushed out by Apple, maybe if it were a bit more streamlined and simplified? Not sure how to do that, since you have done a very good job already of making it intuitive IMO.