That's exactly the testimony I was looking for! Even though they both still have some inaccuracies, James Cameron's 2012 theory and History Chanel's 2013 theory both show the fourth funnel intact after the break:
(At 1:14)
(At 0:45)
Because of the damage to the stern during the descent, I don't think there's any forensic evidence to back up the story of the fourth funnel. We only have testimony and educated guessing.
One of the main witness for the first funnel is Charles
Lightoller. The witness for the second funnel collapse is Jack Thayer, and we can predict that the third funnel fell during the breakup.
Charles Joughin said that the funnel seemed to cant up towards him. I'm not sure if he meant that it fell aft, or if it just settled with the rest of the ship. If its the latter, then it might make sense considering the fact that the funnels were mounted 10 degrees back.