Well, I am so glad I wrote that post because I received a response from a relative who remembered hearing an anecdote about the nickname's origin:
"The story...was that there was an older man in her life when she was a toddler (around 3 or 4 years old) who was named Phil. Apparently she could not pronounce 'Phil,' instead repeatedly and frantically saying 'PidPhiddyPiddyPid!' or something to that effect, and thus, the nickname was born."This is a fantastic story and I was thrilled to hear it! My heartfelt thanks go out to the wonderful family member who shared this with me.