Same problem:
Plex Client Version 8.0.0.17051 beta (change from last post)
Plex Server Version 1.19.1.2645 (same as last post)
The Plex client updated to the latest beta. I check to make sure Enable new video player was set to [on], which it was.
I watched a couple TV show extras that are only a couple minutes long followed by a TV show that is about 44 minutes long and did not notice any playback errors. However, when I returned to the Home screen it had not properly marked what I had watched as played. It marked the first short video and the 44 minute full TV show as played , but not the 1 minute special video that played in between. I was watching these items in a playlist.
Then I ran the same test video movie from the previous post and the error is reproduced: choppiness/stuttering and freezes begin about 40 minutes into the movie until it eventually crashed. The Plex loading screen came on and took me to the home screen.
I started the network logging and here are the logs:
NVIDIA SHIELD plex client 2020-04-21 1833.log (1.2 MB)
Plex Media Server 2020-04-21 1833.log (7.6 MB)
Edit (4/21 @22:15):
Watched a few more TV episodes (local media, not the free Plex streaming stuff). Eventually started to get choppy (froze several times and audio was cutting out) but didn’t crash until I hit the back button on my remote so that it would not autoplay the next episode on the playlist. That is when the Plex app crashed. It looked like the app restarted and took me back to the Plex home screen.
I had the dashboard running on my laptop and it was reporting that the video was still playing (even though it wasn’t playing on any device). Additionally, the timestamp said it was at a duration that exceeded the length of the video. Here is a screen capture from the dashboard:

More logs:
NVIDIA SHIELD plex client 2020-04-21 2010.log (1.0 MB)
Plex Media Server 2020-04-21 2213.log (7.6 MB)
To be clear, this is still with the New Player enabled. I didn’t fiddle with any settings since prior to this edit.