I'm certain there must be a simpler way of accomplishing this, but I did manage to fix it. While working on a separate issue, I discovered that the computer had two versions of ExchangeOnlineManagement module installed (2.0.5 and 2.0.6). V2.0.6 has known problems with some UnifiedGroup cmdlets, so I uninstalled them both and reinstalled only v2.0.5.
All cmdlets are now back to normal output.
Just to clarify: Version 2.0.6 is still in "Preview" (and Preview 6, BTW). Preview (a.k.a. "beta") is always dicey to use on production machines.
I hope you've reported this problem to the Exchange folks at Microsoft!