Arlo,
How about a Facebook Schedule/Event Tab for Facebook?
I can't tell what you're asking for -- please describe it in more detail.
https://www.facebook.com/SilentBark/app/123966167614127/
Other sites like BandsInTown.com, BandMix, ReverbNation etc. have custom facebook apps that allow for gig info to be pulled into a tab on your facebook page (see link).
I'm already using the schedule sharing to push the events to our website. It would be nice to have something similar so I don't have to create FaceBook events as well.
More apps: http://www.bandpromo.me/facebook-strategies/apps
I think a Facebook app could display a listing of your events, similar to the website widget, but wouldn't give you the functionality to send invites, post photos or offer a discussion thread, like a real Facebook event has. I'm not aware of any way to create real Facebook events other than manually on the Facebook website.
Is that your understanding of how these work?