Hi,
I've been looking at those examples too lately.  Is using DockedCells a requirement?  Within a Manipulate environment (which you should assume to use when intending to deploy via CDF) TabView might be a better (and easier) alternative.
Perhaps this might be of use for inspiration or adaptation:
Manipulate[
 TabView[{
   "Trig. Functions" -> 
    Column[{
      TabView[{
        "Sin" -> Dynamic@Plot[Sin[x + \[Phi]], {x, 0, 2 \[Pi]}],
        "Cos" -> Dynamic@Plot[Cos[x + \[Phi]], {x, 0, 2 \[Pi]}]
        }],
      Row[{TextCell["Phase \[Phi]: "], 
        Slider[Dynamic[\[Phi]], {0, 2 \[Pi]}], Dynamic[\[Phi]]}]
      }],
   "Shapes" ->
    Column[{
      TabView[{
        "Disk" -> Dynamic@Graphics[{col, Disk[]}],
        "Square" -> Dynamic@Graphics[{col, Rectangle[]}]
        }],
      RadioButtonBar[Dynamic[col], {Red, Green, Yellow}]
      }]
   }], "",
 Initialization :> (col = Red; \[Phi] = \[Pi];), 
 SaveDefinitions -> True]

I've been experimenting with CDFs lately so I'm quite interested to see any other responses.
Ben