here's an excellent thesis on Earl Bostic -
http://wesscholar.wesleyan.edu/cgi/viewcontent.cgi?article=1786&context=etd_hon_theses which includes a transcription and analysis of "Up There In Orbit"
it should be noted that Bostic had his characteristic sound on "Temptation" recorded in late 1947, Elmer Beechler wasn't in business making mouthpieces until 1950, so whatever gave him his sound, it wasn't the mouthpiece
http://youtu.be/CWSjRW4iu9E
it was probably due to lengthy practice -
"I approached it like a job. I would start [practicing] at 8 o’clock, take a lunch break from 12 to 1 and play to 5, every day except Sunday"
a few quotes about Mr Bostic -
Benny Golson:
"I recall being at Minton's Playhouse in Harlem around 1950 when Earl Bostic came to town and sat in. Coltrane was with me and we heard Bostic play in any key, any tempo, playing almost an octave above the range of the alto saxophone. We talked with him and he told us how each brand of saxophone should sound. He said, 'On the Martin you finger it this way, the Buescher is that way, and like so on the Selmer.'"
John Coltrane:
"I went with Earl Bostic, who I consider a very gifted musician. He showed me a lot of things on my horn. He has fabulous technical facilities on his instrument and knows many a trick."
James Moody:
"He knows this instrument inside out, back to front, and upside down."
Art Blakey:
"If Coltrane played with Bostic, I know he learned a lot. Nobody knew more about the saxophone than Bostic. I mean technically, and that includes Bird [Charlie Parker]. Bostic could take any make of saxophone and tell you its faults and its best points. Working with Earl Bostic is like attending a university of the saxophone."