Ric,
For the second world flight attempt after the extended stop at Miami, your theory about why the lavatory window was covered over doesn't make much sense to me when I look at the path of the sun across the sky for points along her flight path. Earhart's flight during this time period happened a bit before, during, and shortly after the summer solstice on June 21.
At the location of each stop on Earhart's second world flight attempt, the sun rose in the northeast and set in the northwest. At most of these locations, the sun's highest altitude above the horizon on the day or days when Earhart was there actually put the sun slightly north of Earhart's flight path. Here are the specifics for the most northerly stops during Earhart's flight. (These values are for 2014, but they change very little from year to year; 1937 values would have been very, very close to these.)
Miami, FL (Lat = 25.7891 N, Lon = 80.2040 W)
departed 1 June
Sunrise azimuth: 065 deg. T
Sunset azimuth: 295 deg. T
Sun maximun altitude: 86.3 deg @ azimuth 181 deg. T.
San Juan, PR (Lat = 18.4663 N, Lon = 66.1057 W)
arrived 1 June
Sunrise azimuth: 066 deg. T
Sunset azimuth: 294 deg. T
Sun maximun altitude: 86.4 deg @ azimuth 001 deg T
Karachi, Pakistan (Lat = 24.8615 N, Lon = 67.0099 E)
arrived 15 June
Sunrise azimuth: 064 deg. T
Sunset azimuth: 296 deg. T
Sun maximun altitude: 88.4 deg @ azimuth 176 deg T
Calcutta, India (Lat = 22.5726 N, Lon = 86.3639 E)
arrived 17 June
Sunrise azimuth: 064 deg. T
Sunset azimuth: 296 deg. T
Sun maximun altitude: 89.2 deg @ azimuth 007 deg T
Thus, for almost the entire second world flight attempt after Miami, the sun was north of Earhart's flight path for the entire day, putting the right side of the aircraft (with the lavatory window, had it been there) slightly in shadow.
Jeff P.