| Other than getting noiseless pickups, you could try to improve the shielding in the cavity for pickups and controls. I'm not sure how well Fender does this at the factory, but perhaps it can be improved.
If you like to roll off the treble a bit, you won't lose much tone if you get a good set of noiseless pickups, like Lindy Fralins or Nordstrands. I have the noiseless Fralins in my 2003 four string, and they sound almost exactly like the pure singles in my 2008 Jazz V, except they lack some high end "sparkle" and "air." They lose just a tiny bit of that 3-D treble of pure singles, but I only hear the difference with the treble almost all the way up. And even then, I suspect it would disappear in a band mix. I roll off the treble a fair bit, so it doesn't make much difference to me.
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