The people that would need to be contacted is the Defense Pow/MIA Accounting Agency (DPAA)
http://www.dpaa.mil/
There is a contact page here:
http://www.dpaa.mil/Contact/Contact-Us/
From what you have written, I believe the body was recovered from the first burial site along with the "tentative" identification as Harry Parker. The body moved to a temporary cemetery in Serbia and apparently is now buried as an unknown in Florence American Cemetery. They could not make a positive identification at the time, most likely because skull was either missing or there was not enough of it do to dental record matching. The primary means for skeletal identification was the teeth and corresponding dental records.
Not able at that time to make a positive id, he was buried as an unknown. Perhaps you can make contact with the nephew and provide him with your new information. Then he, as a family member can make the DPAA contact.