How do I remove "Other", permanently, from my iPhone 5S?

Question

I have an iPhone 5S, 16 GB, AT&T, iOS 7.1.2. When I plug my phone into iTunes, it tells me that I have a certain amount of "Other". People say that it can be anything from pics from text messages being stored to corrupt music files. Before I get into what it actually going on, I'd like to let EVERYONE know, I have done the following, more than once:
1. Restore from Backup 2x
2. Restore from New 2x
3. I have erased all music files, even though I have NO music on my phone.
4. I have cleared all caches, emptied emails and images.
5. I have run all sorts of programs on my computer.
6. I have lost all my info 3 times already doing backups and restores.
7. I have even been to Apple. They did a restore from new, which is what I told them I already did, and it erased all my "Other"...for 5 whole minutes. By time I got home, I was full on "Other"
With that being said, I look at my usage in my settings. It tells me I have no available memory. I have 12.1 GB used. When I add up ALL of my app usage, I get a total of 1.3 total GB being used by ALL my apps. Yet I have 11.75 GB of "Other". I can't even take a single photo while working! I use my phone for a camera in my line of work and I can't even take one single photo! Yet, after doing a restore or clearing caches, iTunes will show that "Other" goes from a lot to less than 2 GB. But literally, 5 mins later, I walk outside to take a photo and my phone tells me I have reached my limit on storage. I have 7 total photos on my phone. Photo Stream is turned off. WHY? I find it absolutely unbelievable that not one person from Apple can explain what "Other" is. I don't want to hear that it contains this, or it has to do with that...Obviously i am not the only one having this issue, so why can't one employee give us a definitive answer?
Again, please don't reply with any solution that I have mentioned above. I have tried it all, I have been to the Apple Store, nothing has worked. I don't have time to wait at Apple for an hour at a time, when I already have an appointment, just to have them tell me the same crap over and over.  I simply just want a true answer on what EXACTLY "Other" is. My usage in my settings says something completely different than what iTunes tells me.

Answer 1

That is very strange... I wonder if it has something to do with the firmware or some sort of error. I haven't ran into this but at the shop I work at I've ran into several firmware errors on iPhone 4 all the way through the 5s. Maybe its something as simple as putting a different part of the code into iTunes... I know you can something of this extent. I would look up error 1669, I know you have tried a number of things but look it up on the forum and see what fixes are available so that you may be able to restore it properly without all this garbage you are running into. Just a thought for you.