NA Server Issue Idea for Fix
I really think this issue revolves around the League Friends app. It would require a lot of people to see this post, but I think it's worth a shot for everyone to sign out of the League Friends app as a test. If the queue status goes back to normal, then we know it's the League Friends app that needs to be fixed. If not, well, that's simply one variable out of the equation. Regardless, that's less time to find out what is really wrong with the NA queue times.
Edit: If the League servers are connected to the League Friends app, then maybe the servers are just being overloaded with people being on the app.