Your observation is correct: existing objects, even existing button objects, cannot be converted to popover buttons.
As you propose, an existing button object (i.e., one that was created using the button tool) can be replaced by a popover button relatively easily. Any button styles defined for the current theme can even be applied to popover buttons, for consitent styling.
For buttons defined from other objects (e.g., placed graphics), you could either use the graphic as an image fill for a popover button, or use the overlay technique with a transparent popover button. In the latter case, if you're going to be hosting the layout in WD, be sure to place the invisible buttion on top of the grahpic, given the lack of click-through in WD.
Thanks very much. That was very helpful.