Hi, psarkissian - thanks for your reply. I think we exchanged a couple of posts about this on Facebook as well.
My Variax is at the latest firmware revision, with all stock guitar model presets. (I may have tweaked string levels on the Strat settings, but definitely not on the Jazzboxes, where I most often notice the problem.) I'm running direct to Helix via VDI.
Your point about over-normalization makes sense, but it's strange that the pops don't necessarily occur during the loudest note in a given phrase. They're pretty much random, and every now and then they'll even occur in absence of a note (e.g. when the right hand is brought to rest on the strings.) I am beginning to suspect a grounding issue. Maybe the next step is to charge up a battery and retest with 1/4" instead of VDI.