Interesting letter.
Paul L. Briand, Jr's book Daughter of the Sky - The Story of Amelia Earhart, 1960 tells a story of AE going out to Burbank "inspect the new Lockhed for the first time, examining the plane closely; she walked the 55-foot span of the wings, climbed into the cockpit, worked the controls, and started the engines." This makes sense as she and GP were living in Rye, CA, or North Hollywood according to Susan Butler in her biography of AE,East to the Dawn, 1997. Either place (same place?) is apparently close to Burbank. Butler says she "took possession of the Electra on her thirty-ninth birthday, July 24, 1936" but doesn't give a location. Mantz was living in "Toluca Lake in North Hollywood at the time. AE stayed there twice, once for approximately a month, once for a few days, before she and George rented a house for themselves." (Butler). They eventually bought their own house there.
These are the only two AE biography's I have on hand. If anyone has others it might be interesting to check them and see what they say. Neither give any indication of why Mantz may have been in Las Vegas or why he would have been the one to take delivery. Maybe there was some strange rule that only someone certified/qualified to pilot an Electra could legally take delivery. Perhaps AE wanted a Lockheed pilot to make the initial 'shakedown/test' flight since she'd never flown one before and Mantz (and AE?) flew it back to Burbank as her first lesson in the Electra. Maybe she flew from Burbank to Las Vegas as a passenger.
More mystery.