Wow, a lot of people defending poor technique when even the OP wants a different sound.
Playing over the neck is going to give you a muddy, undefined sound, as OP even mentioned. That sound might have some applications, but there are also lots of situations where that sound is somewhere between useless and inappropriate.
When your hands are doing stuff you don't want, the first step is to turn your volume up and make a greater effort to make sure you are hearing yourself as you play. It might mean adding some more upper mids or even cutting a little low end. If your natural tone is so muffled that you aren't immediately aware that your technique is sliding into the mud zone then that's a good starting place.
You might also evaluate how you practice and rehearse, to compare that to what happens on stage. Is there a physical reason your hand changes position, like rehearsing seated and then standing at a gig with your bass in a totally new location, which forces your hand to creep up the fretboard?
Making adjustments to EQ and evaluating posture and practice habits should give some pretty strong clues as to what's causing the issue, so at least you will be more aware when it happens and you can make an effort to practice more disciplined right-hand technique to put it where it belongs without letting it wander around.