i don't use AE that much so i won't comment on that
however, what i explained is exactly possible and seems to be what you are asking for. rather than the major problem being having the 'blades' act as 'buttons' ( very easy in flash ) , it is rather to have the 'button' distinguish between a desired 'button click' as opposed to the 'mouse-down' of the drag and drop.
attached is an example illustrating it all. it was an old fashioned rotating television dial that i created for someone years ago. inside the dial movieclip, which has the instance name 'mc', i placed several new movieclips to act as 'buttons'. these are the 'colored blades'. they in turn have instance names corresponding to thier colors. i also added a semi-transparent mask to give it more of the feel of your original example where only half the dial was shown
4399_rotatingdial2.swf.zip
you can rotate the dial with the 'blades' at will via drag and drop ( you already know how to do that...)
each 'blade/button' is coded to listen for a double click, which will trigger a function, in this case to write the name of the 'button' double clicked in the dynamic text field.
if you are not sure how to target one movieclip symbol inside another, it is done with 'dot syntax'.
therefore the movieclip symbol with instance name 'red' inside the dial clip named 'mc'
would be targetted like this: mc.red
example:
mc.red.addEventListener(MouseEvent.DOUBLE_CLICK, myFunction);
i hope that makes more sense and helps