I'd go with a B'man or SL. Channel 2. Hit it with a nice overdrive, OCD or a Xotic BB Booster. I've spent a lot of time copping that sound, it's one I use on a regular basis. Love the tone, love the player. Audley always sounds good, he's a fantastic player!!!
IMHO, the COD is a little too compressed in the upper mids to do that, not saying it's a bad sound. But that tone requires some "openness" in that frequency range, I think. Bman & SL have more of that. For that reason I would not use a TS style OD either. Too congested, needs an open thing to be happening.