Learn standards, Transcribe (doesn't have to only be bass players) learn scales you'll actually want to incorporate in Jazz ie. Melodic Minor, Harmonic Minor, Major, Dorian, Mixolydian, and most importantly of all; Listen.
I'd definitely check out a Roland Jazz-Chorus, and if the price is too steep, you can find a JC-55 or 60 for a lot cheaper than the 120, also heavy flatwound strings can get you a nice jazz tone.
That program sounds awesome! I'd always wanted to check out something like that. Closest thing we got to that are the jazz workshops in University of North Texas (which I can't afford.) It'd be a pretty good idea to learn (if you haven't already) your Maj7, m7, m7b5, dim. and altered...