I have just the thing for you! I have mapped it to [alt]+[V].
Combined with a macro to move / shift the loop selection right by the loop selection length, I think it is exactly what you need.
the image below starts with the [alt]+[V] macro and loops...
the copy portion already has a default KC... [ctrl]+[shift]+[c]
then shift the loop selection right to the spot you want it. press [alt]+[v]... shift again, this time select the item inside the loopselection and press [alt]+[v] rinse and repeat.