If the Duncan sounds shrill, it may be due to the polarity of the other pups, if there are other pups wired into the circuit.
I can't imagine a full shred sounding shrill, I have one and it's got high mid range and bass, but no crackly treble.
It excels at super high overdrve because it won't fizz out.
Otherwise, if you know that someone actually hacked into the wiring and stripped some of it off, you're better off just buying a new or used one, and letting that one go.
.045 caps might tame the tone if it's really shrill, or try .033. What is the cap value of the tone pot cap, if there is one? if it's like .010 or .022 it's probably going to sound too trebly...
I'm not sure of your pup config, is it HSS? if there are other single coil pups in the middle/neck position they may have a different polarity.
This would mean you'll have to reverse the wiring of the hot(lead) and ground of the neck/middle pups, in order to use the Duncan properly.
You should probably try reversing the wiring anyway. look up the wiring diagrams on the duncan web site, and make sure you have some sort of facsimile of what's suggested. And if that doesn't work, experiment by reversing the lead and ground wires...
You may end up with a thinner sounding middle position sound, but at least your full shred in the bridge will sound better. Another option is to install it upside down (so the words Seymour Duncan appear upside down on the top of the pickup) so the slug polarity is reversed, that may end up sounding better if the pickup had the windings modified on the South pole... That can be done in addition to reversing the wiring. I have a feeling you'll like the sound of that, and it's probably why someone removed the winding, they intended to use it upside down...
I actually think you knew that. Why people post **** like this I don't know...