Hmmm...have you considered an approach halfway between the two? Sure, the sound of a sax is sort of basic, but I can think of a few reed players who've pushed that via electronics, one being the amazing David Jackson, formerly of Van der Graaf Generator. Jackson used saxes (and a flute) fitted with ligature pickups, and fed these through various devices including a Maestro W2, octave dividers, etc. But while Jackson developed these techniques in the pre-synth 1960s and 70s, there's no reason why you couldn't put a modular synth after the pickup(s). You'd need to have an input preamp that can handle the pickup impedance as well as an envelope follower, for starters. Then if you wanted to track the sax's pitch, something like Elby's ED-102 can handle that for both V/8va and Hz/V scalings.
Ultimately, something of this sort would give you the playability you're accustomed to on your axe while opening up a lot of different sonic possibilities that it normally could NEVER have!