Okay, I think I have this sorted out and it's pretty interesting. There seems to be one photograph of the airplane wearing X16020. It appeared years ago in the Letters section of an aviation magazine, I think it was Air Classics. All I have is a crumby photocopy of a clipping. See below. The letter writer found the photo puzzling.
A newspaper clipper reproduced in Carol Osborne and Muriel Morrissey's book "Amelia My Courageous Sister" (attached) solves the mystery. The photo was taken at Alameda on August 3, 1936.
Through the documents, letters, photos, and clippings we have (so far) I've been able to assemble the following chronology.
Sunday, July 19, 1936Lockheed completes the airplane and has it inspected. Lockheed applies for and is granted registration as X16020 but the airplane is apparently marked NR16020.
Tuesday, July 21, 1936Earhart’s makes her first flight in the aircraft. Lockheed test pilot Elmer McLeod is at the controls.
The press is invited and she poses for photos. The aircraft is marked NR16020.
Earhart gives Lockheed a letter authorizing Paul Mantz to take delivery of the airplane on her behalf in Las Vegas, Nevada.
Friday, July 24, 1936Lockheed conveys ownership of the Electra to Amelia Earhart in Las Vegas, Nevada (presumably via Mantz) for $10. (

) A Nevada Notary notarizes the transaction. The document gives the airplane's registration number as NR16020 but the NR is written-over by hand with X. No way to tell when the correction was made.
Monday, July 27, 1936Lockheed notifies the Bureau of Air Commerce that Serial No. 1055 has been sold to Amelia Earhart and encloses an application for re-assignment of license number NR16020 "as executed by Miss Earhart." The application applies for registration in the Restricted category but many of the questions on the form are not answered and it says that NR16020 is the registration displayed on the aircraft. The application is not granted. The application is incomplete and the aircraft has not been approved for international flight so it cannot carry the N designation.
Sunday, August 2, 1936Earhart and McLeod fly the Electra to Mills Field, San Francisco. Until a new application can be submitted the airplane must carry the only registration number that has been approved, X16020.
Monday, August 3, 1936Earhart and McLeod fly the Electra across the bay to Alameda to see Elmer Dimity’s big parachute and fog dispeller. This is apparently the only time the plane is photographed while displaying the X16020 registration.
Thursday, August 6, 1936Earhart submits a new application. The registration displayed on the aircraft is listed as simply 16020.
Friday, August 7, 1936The application is still not right and is stamped VOID. Corrections are made and the application is re-submitted There is a handwritten notation “see corrected application” and another in a different hand “OK 12 mos” with initials. The application is approved. Registration number is R16020.