Can't enable binary logging ("index not found")
It turns out the problem was caused by apparmor.  I had to add the following two lines to /etc/apparmor.d/usr.sbin.mysqld:

  /var/log/mysqld/ r,
  /var/log/mysqld/* rw,


and then run apparmor_parser -r /etc/apparmor.d/usr.sbin.mysqld before restarting MySQL.