How long does it take to Erase All Content and Settings on iPhone 5?
So I verified that deleting the hardware encryption key should not take very long at all. My problem was that the phone was jailbroken on 6.1.2 (not sure what the EXACT problem was). By following this procedure, I was able to delete all content and settings manually, with the file browsers iFunbox and iTools. Unfortunately, it didn't delete the errant configuration profile that locked me out of my phone, so I still had to update to 6.1.4.

I wish I had the time to investigate the issue further, but as this is my primary phone, I just needed it back operational.