I think if it was me, I'd make a whole bunch of layers, and then assign each object to a layer. Then create one extra layer for the original pivot and align a point helper to the pivot of the original. Hide all the layers, Then start at the top and one by one unhide the layer, and center the pivot point to each object. and then hide the layer again. When you've made it to the end of the layers. go back to the extra layer with the pivot point. and make as many copies as you need. Then select one helper at a time and add each one to a layer (add selection to layer in the layers menu). and finally link each helper to the object
it's pretty annoying but probably quicker (at least short term) than learning scripting would be. Of course if you'll need to do this thing more than once it would probably be worth putting the time in to learn scripting.
additionally, you might find this script useful, though I have not used it myself