Both Burt and Paul-Son would have had multiple physical molds for each design and they might not have been absolutely identical. Unless you have the record cards (and the Burt are by no means complete) so that you can date a chip you can’t distinguish who made them.
Also, bear in mind Burt Co never hotstamped a chip in their entire existence. They merely supplied blanks to Christy Jones and Paul-Son.
Paul-Son could have stamped up an order on blanks made years before.
There are no record cards for the blanks.

You can’t get definitive answers for all your questions I’m afraid.