Why does my iPhone keep freezing and crashing?

Hello,

I currently am a Verizon customer and own an iPhone 5 64GB with iOS 7.0.4 installed. It has not ever been jailbroken or unlocked.

Frequently my phone will freeze, sometimes just for a few seconds and other times for several minutes. The longer my phone locks up the more likely it is to crash and reboot itself. When my phone freezes I am literally unable to do anything, no buttons work and all functionality stops. After my phone reboots all seems normal again but this sequence of pain seems to happen far to frequently. It does occur randomly but most of the time it seems to happen when I download something, whether it's an app, update, or podcast even. The larger the file being downloaded the more times my phone will freeze, crash, and reboot, in that order. After it reboots I accept the error message telling me "so and so was unable to download" and proceed to retry. Luckily the download picks up where it left off but may just result in more crashing before it is finally completed.

For the most part my iPhone works perfectly fine. I would say I'm quite experienced with the iPhone and know the ins and outs of it but still I cannot find a solution. I've Googled my issue numerous times, browsed several forums, read many posts of customers with the same issue, followed tons of suggestions and still no luck. I've already disabled background downloads and background app refresh. I have a static background and have already tried disabling the parallax motion. I've manually rebooted my iPhone and tried syncing it to my computer. Nothing seems to work and I just feel like giving up. Some say to just reset my phone but that is not an acceptable solution in my eyes, that's a last resort.

A couple of extra notes -- most of my activity is on my own wireless network and I currently have 246 apps on my phone. I had even more apps before upgrading to iOS 7 and decided to clean up my phone before upgrading. Immediately after upgrading I didn't experience freezing or crashing either, it's only been a more recent thing, like the past couple months.

Is there anyone else with the same issues I'm having? Have you found a real working solution? I desperately need advice! Thank you in advance!