1: You use too much gain/distortion (which sounds awful too...makes guitars sound like rusty chainsaws).
2: There's a dampening device sold on the internet (in fact, I think it was designed by Angelo, to mute unwanted feedback when performing with his 2-necked guitar) which could probably solve your problem without compromising your sound or effecting regular playing. I've seen it advertised before, but I can't honestly say much about it.