FIXED!
I don't know why this root-cause problem happened, but apparently an attempt to "update the firmware" on Scarlett in a previous session failed, and that's what caused the cascading problems with the Scarlett. I just spent about half an hour on the phone with David Joyner at Focusrite's technical support - thanks for the contact info, Tunerman.
David talked me through a whole bunch of steps, including going to some "places" on my computer where I'd never been before (and some dark places where I HAD been before)... we uninstalled/reinstalled drivers (again), made other tweaks that I probably couldn't reproduce now, then successfully did a firmware update on the Scarlett, and now... IT WORKS!!!
I'm creating a System Restore Point in Windows right now...