That's an awesome guitar you have there. I'd be another vote for the Clarity if you're looking to get the sweetest cleans for jazz. Another one that might serve your needs that I use a lot is the Elmsley to get a little more punch. Here's the designer's description:
"The Line 6 Elmsley is a new Line 6 original amplifier that employs a parallel distortion topology that layers distinct saturation characteristics across the lower and upper registers. The Elmsley features a smooth and present bottom end with some exceptional sparkle and definition all through the midrange and above. The result is an amplifier that is dazzling across the full spectrum, and the amplifier deals with pedals in spades.
"The other new key feature of The Elmsley's power amp section is the Negative Feedback (NFB) parameter, where the amount of feedback within the power section's response can be dialed anywhere from wild and unhinged, tight and punchy, and anything in between. As with many amplifier designs, the presence and depth controls are part of this negative feedback circuit and functions to control the brilliance and resonance of the power amp, respectively. As the NFB param is reduced, the presence and depth controls' influences are also influenced, and they become effectively deactivated when the NFB knob is at zero. These interactions allow the player to create countless tonal variations to suit their needs.”