I can report that a dummy VGA adapter really solved the problem. I bought one off Ebay for USD 10 and connected it to a Mini-DVI to VGA connector. I then re-activated the Intel video driver. After several days of use, including shutting down and restarting the NUC, and disconnecting and reconnecting LogMeIn Pro, the video has worked satisfactory all the time. Not the most elegant of solutions, but one that works.
A similar dummy audio jack is required for audio over LogMeIn Pro.