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.