If you get it level with the body, that will help.
A word about trems though.
I'm an Axis guy, but if I'm not mistaken, the trem on a JP is a floating and non-locking trem. The trem system is rounded out with locking tuners on the other end.
I don't know how aggressively you are using your trem, but this system will go out of tune if it's used frequently or aggressively.
Here are a couple problems with this type of trem system.
1) If you do not have a locking trem, the ball ends of the strings set in the trem block in a little hole. When you use the trem, you release the pressure holding that ball in place, and it can move and shift, knocking your string out of tune.
2) Locking tuners are a great tool. They eliminate tuning problems associated with traditional tuners in that the "spool of string" would loosen and tighten every time you used the trem arm, knocking the strings out of tune.
The problem with them is that there is a legnth of string between the tuner and the nut that can get "bound up" on the nut a little bit. When you use your trem, the string slips across the nut, which can knock your strings out of tune if the string doesn't return to it's original position. I think the JP model uses a graphite nut to help prevent string binding on the nut.
3) The floating trem. In order for your guitar to come out of a dive-bomb in tune, you need a degree of tuning stability. Meaning that your trem will return to point zero when you're done using it. In a floating trem, the only thing that returns the trem to point zero is the balance between string tension and spring tension, so when ALL the strings are in tune, the trem springs are adjusted to return the trem to point zero. Like I said, this is dependent on all the strings being in tune. If one of the big strings gets bound on the nut and goes sharp, then all the other strings go flat to a degree.
You can lessen the effects of these problems through various means.
You can oil your nut to decrease friction. You could use Fender Bullet strings to reduce the effects of the ball-end problem. And you could install a Hip-Shot Tremsetter to ensure your trem returns to point zero every time.
This is why I prefer a double locking trem, such as a Floyd Rose. A Floyd locks down the string right at the end of the vibrating length of the string at each end.
parallel bridge ~lube nut and lube the bridge screws,( lightly,peizo in there),and bridge pivot studs and yes stretch strings works wonders!,also if you don't pull trem up you may want to block trem it does 2 things ,make the trem more stable for bends and dives actually transfers more vibration into body a little bigger tone!Check these out idiotproof to install and hidden and removable!