I'm afraid that the factory data reset is the next step. If this doesn't fix the issue, then you'd have to do it for Verizon anyway before they will replace the device. They should be able to see that you've already done it if and/or when you call them again.
Before you jump on the FDR, let's try this. Does the status bar show normally when you choose the EASY MODE for TouchWiz (SETTINGS/DISPLAY/EASY MODE)? Or better yet, download a third party launcher like Nova, Apex, Action Launcher, etc. See if the status bar comes back. If it does, then your stock launcher (TouchWiz) or some of its components could be corrupted. Since you've already tried safe mode, which isolates non-default settings and third party apps, an app or setting conflict likely isn't your issue. If the alternate launcher restores your status bar, then try the stock launcher again to see if it was somehow jarred into working again. It could be something as simple as a library file or a service holding bad data that gets cleared out.
If that works, great. If not, then you're back to the FDR. If you have to do the FDR, resist the temptation to restore from your cloud backup and build the phone as though you've never had one. If the issue is a data file or a setting (unlikely in this case), you stand the chance of putting that bad data right back on the phone.
The only other option that I can think of is to reload the OS. This is relatively painless because it just takes a little bit of time plus the rebuilding, of course. If you're not up to it, then perhaps it might be time to ask Big Red to replace the device. Note that it will very likely be a refurbished device.
Reloading the OS may be the answer because it will actually replace the OS on your device, not just clear all the data and apps like the FDR does. If your launcher is bad, it's a good possibility that other features are bad too and you've just not yet noticed. You've got a few options for this. One, use the SOFTWARE REPAIR ASSISTANT feature in the Upgrade Assistant app that Verizon installs on your PC when you connect it to your phone. Two, use Samsung's Smart Switch which does the same thing. Both will download and install the correct OS for your phone. Then you get to load up from scratch.
Good luck.