You sounded like this looks, too?!?

I thought about a static hand position and even tried just playing muted strings with no defined notes… But, well, one, I think the fretting hand movement seems to help with the string-tracking somehow…? And two, well, that would sound like absolute garbage with distortion, and when I’m playing my Strat, I LIKE distortion. 
I’ll just come at it two ways - full-tempo “damn the fretting hand!” picking practice, as well as gradually working up from, oh, I can probably play this cleanly around 120-140 or so, and just racheting up the tempo gradually thhere to pull the fretting hand up to speed.
I also tried this Satriani style, reaching over the neck with my picking hand to mute the strings, and tapping them with my fretting hand - a Strat probably isn’t the guitar for this, especially running into an amp that isn’t all THAT distorted, but maybe on one of my RGs that would be a good way to get the fretting hand movements up to speed.