It's really hard to tell Dave but from the sounds of it what you've described is almost as if a noise gate is hard switching in and out, there isn't by chance something in your chain inducing that?
Also, that Eventide's a pricy box, would think it's clean and no auto-noise reduction involved, even a slightly low input signal should be okay. Most often units have a -10 db and +4 db input/output toggles and if the unit in the chain prior to the Eventide is running at -10 db, you're getting what you should as a signal. If your in/out chain has a anything using +4db will often induce noise especially when chained.
The way you described noise when you pick, sounds like something is either not up to snuff (a DSP is failing or is just plain noisy) in something of the like but I'm guessing at this point.