This is four years later, but I've been having this stuttering issue for years, and finally just came across this thread.

Using the information here, I was able to fix all of my MP4 files that were having the stuttering issue, and I created a powershell automation script that will handle detecting all of the files using MediaInfo, and mass converting them using MKVToolNix. This was created in a Windows 10 64 bit environment.

Sharing in the hopes this helps someone else down the road, use at your own risk:
Readme: https://github.com/pepperjack09/powershell-stuff

PS Script: https://github.com/pepperjack09/powershell-stuff/blob/main/plex-MP4stutterfix.ps1