I did try this for the last few days and it did fix the stuttering issue. Looking at the dashboard in PMS showed that the video portion of the file was now being transcoded. When using the new video player the video portion of the file was direct played.
A development on the above happened today. PMS updated to version 1.19.5.3112 and the ATV Plex app updated to 7.4. As an experiment I switched the video player back to the new version and played a couple of files. So far all seems well and the stuttering has gone. The files I played were both MKVs. One was a rip from a DVD (done using MakeMKV) without any additional processing. The video codec is MPEG2VIDEO and the audio is AC3. This file direct played without issue. The other file was ripped from a Blu-ray (also using MakeMKV without any additional processing). The video codec is H.264 and the audio codec DCA/DTS. Again, this file played without issue.
Hopefully the updates to the server and app (or at least one of them) has fixed the issue with the stuttering which has been present for the last couple of weeks.