I decided to find out if it was the MP4 video codec I was importing that was the problem. So, I uninstalled the video engine, did the Trasher Dance, rebooted, installed the video engine again, rebooted. Then found Shutter Encoder which is a free/donation transcoder:
http://www.shutterencoder.com/en/
I first tried to transcode the MP4 to DNxHD, but that didn't work, I kept getting an error that the file was unrecognizable. Then I transcoded the MP4 to H 294 and set the extension to mov. Imported that and, so far, no errors yet and I've quickly started and stopped playback repeatedly over a couple of minutes and no problem. After a few starts/stops I was getting the error "The Avid Video Engine stopped unexpectedly" with the MP4 import.
Note: You will have to go past a couple of Windows warning dialogues as the Shutter Encoder installer is not signed to Microsoft's liking, but once past those warnings it will install. It appears to be a well designed program with crisp dialogue windows and a very sharp video window. And there is a lot more you can do with it besides transcode video codecs.
While it is donation, you can pull the slider to the left on the download page to $0. If this works I'll probably donate later, but not as a trial.
As always YMMV.