This post is old now but I just realized I never gave an update on how this turned out for me....
I ended up ignoring all the good advice you guys tried to give me (It was good advice!), and I performed surgery on my controllers. I ended up getting both of them to work just fine. My R2 and L2 buttons are now more sensitive than normal since I ended up removing the spring in both of them, but other than occasionally causing me to waste a few bullets in Destiny, this has not been a problem for me at all. It was also very easy to do. Sending the controllers to Sony is probably the best option, but I went from having no working controllers to two, so I'm satisfied.