Hey Guys,
Went to the Apple Store today, and Touch ID works, hopefully it will continue working. The Apple employee who helped me first ran a diagnostics scan. The scan showed that I had 15 of the native apps crashing, he said that he had experienced this issue before. I was told it was primarily due to a bad iOS install and that it's possible my phone was like that out of the box. He said that this could be causing the Touch ID issue, but he wasn't ruling out a hardware issue, yet. He then made me do a complete reset, setting up my phone as a new iPhone, to fix the issue. I then proceeded to try using Touch ID, which failed to work for me again, even though it worked perfectly for him. He then stated that he had "never seen this before," and told me that they would replace the entire front of the screen (apparently they can't just replace the sensor.)
The repair was done in-store, took about 1 and 1/2 hours, and cost $0 due to the 1 year warranty. (Regular price $129) I came back an hour later, setup my phone again, and so far Touch ID is still working well.
Since I also had the software issue that I stated above, I kept my phone setup as a new iPhone. I just re-entered my Apple ID, downloaded apps, etc.
Hope you guys can get your phones fixed also,
Jordan