Skans, I know exactly how you feel.
Or I did till I cracked open my Spectre after 1000 rounds. Half had been on a pistol, half had been on my buddy's F/A trigger pack 10/22. Lead fouling, lead fouling everywhere! But that's why it's designed to be taken apart, right? Right.
I have tried picking, wire brushing, wire wheels on my Dremel, Hoppe's 9 soak, and the infamous Dip. Haven't had the gumption to make a batch of Ed's Red yet to try it.
You know what works the best? The Dip
(image owned by Disney)
For the love of God, if you are going to use the Dip, make sure there is a place local to you that will dispose of hazardous chemicals and don't breathe the fumes. Also, don't use the Dip on anything other than stainless parts. Actually, you probably just shouldn't use the Dip.