I have no idea. Roosevelt got in there by chance, but had the will of the people to back him up. He also had the press on his side, which is a very different beast today than it was back then, but again- I do believe the press, like Congress, will follow the money, and if the people get active enough to speak loud enough, both the press and Congress will respond if only for fear of losing their jobs.
Roosevelt only did the third party thing later, after he was dissatisfied with Taft’s performance. Whether or not Bernie would do that, and whether or not there’s enough people to support a third party yet, I don’t know. Probably not in 2016- but I could have never predicted, in 2008, that a man like Bernie Sanders would be as successful as he is today- so clearly that number is growing. Someday soon, the viability of a third party might be a thing to reckon with, finally. If you’re right, and the current parties will never change their habits, then that’s really our only hope.