Check the battery in your JPX. When it gets low, the whole guitar will sound like crap if you're using the blended output.
the piezo signal is very hot compared to the magnetic output on the guitar. with my jp guitars, my axe ii input gain for the mag pickups is about 30. i tried the piezo through the front though and i didn't experience any distortion.
can you try the piezo through anything else to see if it also distorts there?
when you use 2 separate cables, you lose the function of the "mix" control on the the piezo controls, and it seems that the volume of the piezo is the same as with the mix control turned all the way up.