Do any of these programs back up and restore texts? I've tried to research a few options for restoring texts but they all seem to have limitations
Funny you ask that. TiBackup does actually back up text messages and call logs now, they updated it like 2 or 3 days ago... maybe less.
ALSO, for the OP... If you are backing up your phone already to your account, you kind of have a phone back up. Kind of.... What you have is upon signing into a new phone, the Market - Google Play - will auto download for you all the apps you had on your old phone. Some times it gets them all, sometimes not, but sometimes it even gives you ones that you already had deleted. It's not much, but its something.
Things like your ringer, your volumes, saved wifi passwords, that stuff will all auto repopulate with the automatic backup/restore functionality of an Android phone, but the settings and preferences for ALL apps will NOT come back and you'll have to do them manually.