AFAIK this sort of thing doesn't really go away. The only way I've gotten a nylon string to quiet down is to rough up the surface with fine grit sandpaper. I wouldn't recommend it though, it does weird things to the tension and sustain.
I did notice though, that if I ever got stuck plugging the pickup straight into an amp with too low of an impedance that that squelchy fingerboard noise got much worse. (This is probably obvious).
Raising the action helped some. EQ'ing out some high mids did too.
YMMV, IMO, de yadda de yadda
