Problem in OP still not solved with Windows 10 and Garmin Express 7.2 in August 2020.
I solved it by following a suggestion above: closed Express, disconnected Forerunner 305, restarted Garmin Express 'As Administrator', reconnected Forerunner 305.
The sign-in screen froze after entering email, pw and hitting the sing-in button. Closed the sign-in window, re-clicked to sign in, reentered email and pw and this time it worked.
There is no excuse for an obvious and destructive bug not being fixed 5 years on, tsk tsk Garmin.
Jack