My user account was indirectly a member of the ora_dba group, via my administrator rights, but it seems I need to be directly a member of the group to login / as sysdba.
That said, the short, bullet point method is as follows:
Rename the current password file pwddbadb01.ora to pwddbadb01.ora.keep.
Copy another password file, for which I did know the SYS password, to pwddbadb01.ora.
Sqlplus sys/known_password as sysdba.
Rename pwddbadb01.ora.keep to pwddbadb01.ora.