The ESP Eclipse can do it. And the LTD EC-1000 isn't that far behind. I wouldn't knock the EMG 81/60 combo until you tried it, either. It is more versatile in a LP design since the thick body has so much natural warmth.
In my experience, you'll never have true max shredability unless you have a 25.5" scale (and preferably a bolt-on or neck thur design), but the Eclipse is a seriously hot rodded LP and brings huge, girthy tone into the equation, which many shred guitars lack. The actual selling price of new Carvins is quite high, but they can be fantastic values when used. The CS and CT series guitars are prime for what you describe, and the ESP Horizon is an interesting fusion.