Happy to report that the issue has been resolved.
Turns out the problem was that the Steinberg USB Driver that came with the UR22MkII was not totally compatible with either High Sierra or Mojave, the two OS I’ve had on this unit (currently the latter). There is an updated driver available by download from Steinberg Support which fixes the problem. I downloaded and installed the updated driver (1.10) and all is now well.
Thanks to everybody who chimed in on this, and kudos to Apple Support for tracking down the problem.
–Len