No rewiring is necessary for this circuit. All you have to do is to find a way to discharge those caps one at a time.
Well, more like "in parallel" which is what the ICL7660 does. Take a look at the data sheet; it does what you describe with no rewiring, just switching.
Again, the circuitry that is in my 90% complete patent application does not use current dividers or voltage dividers.
Right, neither does the ICL7660. A doubler (or halver) is fundamentally different than a divider.