I was also locked out of my 60E, but was able to get it to reset to factory settings.
Hardware: FortiGate 60E
Firmware: v5.4.0,build5335 (GA)
Issue: Lost admin password
Resolution: Unplugged the 60E, waited 10 seconds, pressed and held the Reset button, plugged the power cable in, held the Reset button for 60 seconds.
Result: After performing these steps, I was able to log in with default credentials (username 'admin' and blank password).