I've had many problems with my JP Majesty. It's not crisp/clean sounding. Very fuzzy sounding no matter what channel I'm on on my amp and on top of that I get this weird overtone whenever playing the G string making me constantly sound out of tune.
Where do you live? Did you buy it new or used? It may just need a setup (who knows who adjusted what before you got it) or it may have another issue.
If new, you are under warranty so bring it back to the store you bought it from and have them check it out. You can also contact Ernie Ball customer service (see the link in my signature below).
I can't address the G string issue, but customer service can help.
Regarding the fuzzy/not crisp-clean sound, the Illuminators are fairly high output pickups. Have you tried rolling down the magnetic pickup volume knob 1/6-1/4 turn? And if the piezo pickup sounds fuzzy, there are controls on the back cover of the control cavity.