I just think that even WANTING to put a sax sound across the whole keyboard is questionable. Why would you need that amount of range for a sound that only spans a few octaves?
The way to make non keyboard sounds realistic is to restrict yourself to only playing them in their natural range, and idiomatically. In other words, a sax never solos on top of a chord of sax players playing an octave or two below him! Saxes tend to have very close voicing (the melody intelligence feature on many arrangers is a wonderfully easy way to emulate those kinds of voicings).
If you are trying to play a sax sound pianistically (two hands, whole keyboard) I am afraid it will never sound right. Use your left hand to play chords for the arranger, maybe a soft piano/string layer or pad, and play the solo sound as a split.
If there are too many button presses to go from full piano full keyboard to split piano/sax, consider making two different registrations, and just hold the style and tempo as you change.
Just remember that each and every sound has it's own unique way of needing to be played. Piano licks are no good with an organ sound. Sax solos with a bender don't work with electric piano sounds, a Wurlitzer EP has different voicing needs to a grand piano....
The best way to nail a good sax solo is to listen carefully to a real sax player for quite a while! Until you understand what a sax player would NEVER play, you will always find yourself doing exactly that, and spoiling the whole effect.
The T2's SA voices represent a revolution in ability to shape a phrase with legato and staccato playing. BUT..... you have to understand when and how the original instrument would play these techniques before you are going to be able to use the keyboard for a convincing solo.
You only have to listen to the factory demos to understand that, with time and skill, YOU can make it sound that good.....
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An arranger is just a tool. What matters is what you build with it..!