I don't agree with you about 16 hrs isn't much. The DO I shadowed told me its basically pointless to shadow more than a couple of hours because we aren't medically educated so most of the time, we have no clue whats going on. All you see if the doctor-patient interaction. I shadowed for about 40 hrs but I felt I didn't learn anything past the first 10 hrs. Plus, its called shadowing, all you're doing is standing by watching the doctor work. So I believe that the 16 hrs is enough.
Also I think you should ask the doctor to write you a letter after the first week and tell him/her your situation so they will understand why you need the letter so soon. Be bold, thats what I did and it saved me a good 2 weeks so I wasn't as late as I could have been. I started shadowing the first week of September and I got my DO letter sent out by the end of the second week of September.