Do you have a disaster recovery plan? If you have offsite backups, it should be trivial to spin them up on a different host (assuming you have an emergency backup host, right?) and redirect DNS.
Have you considered sending out an email to let everyone know that your service is down?
I know you can do this, because I receive promotional emails every day. If your support department can’t do it, contact your marketing department because they’ve got it figured out.