Hi Blake,
Thanks for using the Apple Support Communities. Based on what you are describing (the Wi-Fi settings becoming unresponsive) and the troubleshooting steps you have already tried, you may want to try reinstalling a fresh copy of iOS to help resolve (or at least rule out) any system software issues. This is different from a full "factory" restore, in that it only reinstalls the operating system software and doesn't affect your personal info (like files or contacts). Once iOS is reinstalled, you will want to test and see if the issue persists or returns. The process is outlined in the following article under the section "If your device turns on but gets stuck during start up" (the article itself is aimed at a slightly different issue, but the steps outlined are still applicable in this case):
If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support
Note: While this process generally shouldn't affect your data or settings, it's always best to have a full backup of your data just in case. If you haven't recently backed up your device, you may also find this article helpful:
How to back up your iPhone, iPad, and iPod touch - Apple Support
Regards.