This is one of many reasons why people who have no business installing beta software should NEVER install beta software on their devices.
iOS betas have always expired, going back years, and this has always been documented in the release notes. It's also made clear in the release notes that you can't upgrade via iTunes to the public release from a beta - you have to manually download the IPSW and update it yourself.
So just download a "production" iOS 7 IPSW and "update" to it.
That's what I did to update when the iOS 7 GM came out, and I've used it in the past when I unintentionally let an iOS 6 beta expire.
[1] http://www.jailbreaksquad.com/wp-content/uploads/2013/01/Bro...
A quick jump onto developer.apple.com to download the latest IPSW and my iPad is working again.
I backed it up and within 20 minutes it had been disabled.
Interestingly, it put it in a state in which it was unable to ring for incoming calls.
I wish Apple would not report that your iOS version is "up to date" in iTunes if you are running a time-bombed beta build. Even if they don't want to support a direct upgrade path from beta to GM, they could indicate in their software that your software is not up to date.
Not everyone can afford dedicated dev devices--even though that is in their terms of use.