Calendar Remind Type of "Alarm"

Google Calendar (Android and web) has two reminder types: Notification and Email. So far so good, but they need a third: Alarm. Alarms on Android typically work the way you would expect an alarm clock to--they go off, no matter what state the phone is in, including muted for the night.

I would like to be able to create an event, set a reminder type of alarm, and have that result in my Alarm app ringing for the set time. My main use case is for unusually early meetings; the current work-around is to set the alarm manually.