Thanks for the reply Curt, but that's not true. The installer would not work with simply the serial number of the qualifying product (which I had and tried).
I found a solution on my own for anyone else that might be interested:
I had a backup copy of the hard drive file folder that contained the "Photoshop Installation" on my old computer. I copied the entire contents of that folder from my backup disk to my new machine and then told the installation program to verify my upgrade installation by checking that specific folder for the older qualifying product. It accepted that my machine had a previous valid installation and proceeded to fully install a fresh copy. Problem solved.
Message was edited by: McLainStudios. Fixed typo.