All of my text messages have disappeared on my iPhone 5 running iOS 7.1.2?

My phone has been on the fringe of running out of storage for a few months, typically hovering between 500 MB and 1 GB. However, my messages suddenly started to glitch, so I turned off my phone and turned it back on, and my messages were no longer showing in the messages app. I checked the usage section in the general settings, and the messages were still present and taking up 1.8 GB of memory, as they had previously been, but I could not view any of these messages. I searched for them in the spotlight search and I could see them there, but when I clicked them it would direct me to my blank messages app.

So far, to no avail, I have tried:

Hard Reset (holding home and power button for 10 seconds until phone restarts)

And selecting 'Erase All Content and Settings' in the settings and restoring my phone from a backup.

After performing these procedures, my phone has jumped to 8.0 GB available (most of which appears to have been app cache and unwanted music), but the 1.8 GB of messages still shows up in my usage settings. The only difference now is that the messages no longer appear on the spotlight search. At this point, I'm unsure of any other procedures I can perform to recover these messages, as they still appear to be present in my phone, just not visible.

And lastly, would calling Apple be a viable solution, or would they just suggest to do what I have already done?

Try FoneLab. It allows you to recover accidenatlly deleted or lost files like text messages, contacts, notes and more from your iPhone.

When your iPhone run out of storage, iPhone will auto clean up by itself. It will clear some document &data from all apps including Message.app. I think it deleted your some message attachment, somehow the message.app can't restart again. So that it is. You can clean up your iPhone with an app Named "CleanMyPhone" next time.

What time does your last backup? If you restore your iPhone from a backup, your everything will be replaced of the backup content. And the 1.8GB message is your backup message.
You need to export your message content with some tool app.
http://www.datarecoveryforiphone.com/ios-data-recovery.html

Actually there are 3 ways you can try to recover those messages
1. Recover them if you have iTunes backup
2. Recover them if you have iCloud backup
3. With the help of some 3rd party tool if you didn't have any backup in hand. Just follow the source which introduce how to use Dr.fone to recover the lost message which I tried and actually worked for me.

Hope it helps.