active P pickup in my Peavey Foundation S is fuzzy

[Pickngrin]

I've had this bass for years, bought it used in the early 90s. It has 2 active pickups, P and J style. I find that the P pickup always seem to have a fuzziness to the sound, whether plugged in directly and through headphones, or into a bass amp. It's not like a hum that goes away when I touch the strings, but a fuzziness to the sound (without any overdrive). The cavity barely has any shielding, just a thin strip of copper. Would shielding likely help this? Is it possible that the active pickup 'went bad'? Any ideas?

Thanks!