Per Obihai tech support these two techniques accomplish the same thing, which is good to know.
They both factory reset the unit, but if for instance there is no dial tone on your phone, dialing ***81 will not accomplish anything.
Best Regards,
Obihai technology
More from support:
Charles, the AC adapter should be plugged in when you do the reset.
Best Regards,
Obihai technology
That means the awkward juggling I did wasn't necessary after all.