you need the so-called "video information". start here: https://www.b4x.com/android/forum/threads/exoplayer-youtube-dash.75195/#content
you'll start with "v=T6vELKGu-GA", extract the video information, parse it and back yourself into the long url form you are familiar with.
(note: the easiest way is to get the free youtube api key and play the video in its own view. you can switch back to the exoplayer view for your regular videos. if a video provider whose videos i want to see only broadcasts on youtube, my app just switches from exoplayer to youtube player. works fine.)