Thanks for the info! By my reckoning, the #27 cornet mouthpiece would have been about 1.5 mm deeper than the regular Heim one. Your comparison to the Bach 7A (deepest of the 7 cups, thanks Mike) would mean, Bix still preferred a deep mouthpiece by mid-1928. And the use of a rather narrow Bach 10C which Brad saw, would certainly have confirmed a loss of stamina.
About the Bach #620: lucky you! I wonder if the 7A from the Beiderbecke family estate (which Evans mentioned) is the Mount Vernon one? Anyway, I suppose it would be in the Bix Society's collection now: http://www.network54.com/Forum/27140/message/1195665172.
Frank
PS Speaking of deeper mouthpieces, here's what Pee Wee Erwin had to say about Charlie Margulis' choice of equipment in his foreword to "Charles Margulis - The King of the Mountain": "He always played a medium large bore Besson trumpet, one of which was a beautifully engraved gold instrument with jade buttons made for a Paris exposition. His mouthpiece was a deep V cup with inside diameter approximately the same as a Bach no.3. The fairly wide, flat rim had a slight bite on the inner diameter."