Hi Erik,
Well, from your extended description of the problem, now it sounds that it's clearly RFI. You said your guitar had humbuckers in your original post, but you may have just mentioned the culprit...single coil pickups are by nature really susceptible to RFI.
Putting a TRS cable between the Mesa preamp and the Zed wouldn't do much beyond lowering the noise floor if the preamp's output is balanced. To find a ground problem, you'd need to lift pin 1, which is the "pin 1 issue" Cactus Music mentioned above. That's what a "lift" switch does on a DI, which was why I was suggesting you try that. There's no "pin 1" to literally lift in a firewire or USB cable, but there are cables you can get that do essentially the same thing. As for AC lifting your headphone amp, you'd be much better off getting a pin 1 lift adapter if the inputs are XLR, or one of those Ebtech Hum Eliminators if they're TRS.
Anyhoo, looks to me like you have garden variety interference on ye olde single coils.