Please could you re-do the tones with a regular guitar?
if I would use a not digital guitar, I would use a Gibson ES-175 or a jazz Ibanez..
but at the moment I don't have any of the 2, I had them in the past..
from what I remember they sound quite close to the Variax jazz box model I used to do this patch..
if you have a regular jazz guitar you should roll back the tone knob at some point, not too much and not too little, you have to find the right spot, depending on your guitar specific voice..
if you have a Strat type guitar equipped with single-coils forget to get this tone in a convincing way, I think it's impossible..
if your guitar has a neck humbucker you have some hopes to get somewhat close, but probably you'll have to adjust a little the amp drive setting depending on the signal strength of your guitar..
think that typical jazz guitar humbuckers are less powerful than those of a Les Paul or a 335..
that's all I can do and say to help you