Turns out every lead I was following was a red herring.
I had another function hooked into wp_insert_post that was redirecting you back to the Video single page instead of sending you to the Thread single page if you posted your reply FROM the Video single page. It turns out that redirect was hitting and stopping execution before the bbp_new_reply actions were allowed allowed to fire.
I changed that function to also hook into bbp_new_reply and changed its priority to 11 so it would run after the native actions. Working great!