Thanks, I manged to find the Lopez recording. Though not the Rolfe Edison...
The range is a matter of technique. Even a piccolo trumpet wouldn't have that odd, peanut-whistle sound. Its an impressive feat, but the tone produced is diminished to a squeak by the means employed.
Looking around earlier today. I found some posts about historical Cornet/Trumpet technique. It was Armstrong's sustaining his full tone and volume all the way up that made him stand out. The reference mentioned this around the famous 'cutting session' between Armstrong and Jabbo Smith. Smith could play as high as Armstrong, but his tone (like almost everyone's) shrank the higher he went.
Armstrong, Roy Eldredge, Bunny Berrigan, all jump to mind as examples of sustaining the full breadth and depth of sound all the way up.