I'm in the camp too of playing with your pickup height. I set my main P bass strings at a 7.25 radius to match the frets, and set the spacing at 7/64, which is the norm. At that point I start playing, and tweak the pickup height to get the strings even sounding.
As stated, to get the E and G strings to sit in the mix better, either move the pickup closer to the strings, or move them down and away from the A and D strings.
Keep in mind if you were running active pickups on your Jackson, the passive P bass pickups are going to sound different, especially if you had an active 2 or 3 band EQ. You can either tweak the pickup height setting, which will get an even response, or go with a set of active pickups, like EMG's, or an active preamp.
Good luck, and ask more questions if you need help.