For what you're looking for, you should keep your exisitng landline (POTS) service and not switch to Uverse Voice. You'd have separate bills, but you'd keep your existing landline pricing and have service beyond the 4-6 hours the back up battery would provide.

Since you mentioned you're in CA, it jogged my memory that nonpublished listings were much cheaper in CA due to old tariffs and Pacbell pricing. I only handled CA landlines for a couple months, so I didn't think of that earlier. Uverse is nationally priced, so CA customers don't get the breaks they used to.