As Adam said you can use an automation to copy records over there. That would be my suggestion as well. Since the records are likely not going to be modified first (to trigger a regular automation)the best solution I see would be to have the automation run every day on a schedule and copy records that are late as of that day([due date] before Today). You can even just do a few fields so keep it easy to read. Since it will be related back to the original record all you would really need is the due date, the record id of the record to be turned into the "related record" and whatever else you want to show.
Does that make sense? Sorry I would have replied earlier but I got caught up in something.