just make your simpleexoplayerview fill the screen (i used the designer, but it would probably work by hand: 0%x,0%y,100%x,100%y). when you turn the device on its side, you'll get fullscreen. (you can't get full screen in portrait mode for obvious reasons.) i usually start viewing in portrait mode, but if i'm going to continue watching a particular channel, i flip the device and prop it up on the table to watch fullscreen. no problems flipping back and forth.
there was this link from a year ago:
https://www.b4x.com/android/forum/threads/fullscreen-in-exoplayer.102117/
regarding the "FILL" setting. seems that it worked for others. not sure why it doesn't work for you. what i do works for me, so give it a try. or check the other thread to see if you're using "FILL" the way it was suggested there.