I know exactly what you mean Randy. I too change my style when playing bass. My style of playing in improv tends to lean towards the melodic. One part of it is expectation (what the audience expects to hear from a particular piece of music given its style), another is simple ergonomics (long bass rods & springs will simply not have the same response as soprano rods & springs for example), and the third part is the voicing of the horn itself.
For me, my approach to all the saxes I play (sop thru bass) is very different. I see each as a unique instrument, and play each slightly differently. For example I generally use different riffs, licks, etc on each. This allows me to sound like a tenor player, bari player, etc. , rather than a tenor player playing baritone, and so on. When I play bass, I see it as a completely unique voice with really no contemporaries. Because there are no reference points out there for the audience (since very few listeners are familiar with any bass sax players, and those that are, know them from a different era, and totally different style, so it really isn't a reference point anyway) I can pretty much do what I want and almost get away with it. ;-) And since I don't play bebop, I don't run into the "You're playing what on bass?" thing. I'm a blues, R&B, rock, & lounge jazz type player (the last one reluctantly), so on those occasions when I do hit bad notes, I usually joke and say "I'm playing outside then changes", and that shuts everybody up.
PS: I loved your rendition of Donna Lee on your Eppi bass. I would love to see you play it on a vintage bass though as well. It would be interesting to see how an accomplished bebopper can play a piece like that on an old, ergonomically-challenged bass compared/contrasted to the new state of the art model.