I have an MIM P and although a lot of peeps around reckon the pups are weak, I really like the sound of mine, trad P Bass thump and growl and noise free. I'd try some rounds (RS66), dump the foam mute and play around with your amp eq. Theres not a lot to the controls on a P... I normally have the 'tone' set halfway so I can adjust on the fly.
Jazzes are nice also.