The first photo here was taken on May 20, 1937 at Burbank, the day after the airplane came out of the rear shop. This is one of the Dusty Carter photos owned by TIGHAR. They're the only known photos of the "secret" departure of the second world flight attempt. You can clearly see that the lab window is still present.
The second and third photos were taken in Miami as AE taxied out for departure on the morning of June 1, 1937 - the public beginning of her second attempt. The shiny patch is apparent.
The fourth photo is how Bill Harney portrayed the patch. The positioning is correct but the rivet pattern on the patch itself is pure guesswork,