I understand where you are coming from and you have a valid point, Bob, but though it was chosen to be played at a lower octave by the performer because he liked it that way and wants to continue to play it that way, kind of trumps the orchestration of Glenn Millers original manuscript in this case.
My point was that even if lostlobos wished to continue to play that way, one could separate spatially in the stereo image, have his right hand on the right side and the left on the left side, and get a near infinitely variable level of separation on the channels based on desired results. Ive done that many times in varying amounts and the effect does accomplish the effect I was talking about in the original post. Also, with equalization, one can lower the low-mids of the right hand and deepen the lows of the bass on the right hand and increase that difference and of course adjust volume independently as well.
Most amateurs wont invest in as complex a set-up to accomplish these goals, but I was answering Mats queries that it was possible without changing the way lostlobo liked playing it, thats all I was trying to say. Of course the registration or octave could be changed as the easiest/quickest suggestion is not a terrible idea.