Gotcha. There may be something to looking at video card drivers and stuff like that. But I'm still convinced it has something to do with the HDMI and at least the resolution settings used, etc. As a note- unfortunately you will see very different results from testing with Win Media Player or just the basic Windows desktop output vs. a program like MediaShout which utilized DirectX to route signal to the screens. Since MediaShout functions more like a video game instead of a desktop computer application, it by nature uses more resources than a consumer video player like WMP, as it's sending video down the line. This can cause digital video connections like HDMI to freak out a little bit. To give an example- it's kind of like talking to another person through a PVC pipe. When the pipe is pretty short, or the words are very simple, it's easy for the other person to understand what you're saying. But if you increase the length of the pipe, it gets harder to understand what you're saying on the other end, even if you speak louder (like a signal amplifier would do). It is also more difficult to hear at the other end if you speak in more complex words (like running at a higher resolution). And with HDMI, it's a "smart" or digital cable/connection, so that means instead of still working but looking bad on the other end (like when there used to be a bad svideo or VGA cable, it would look grainy, blurry, or the color would be reduced), it just doesn't work at all, or looks perfect but then intermittently stops working/goes black. That will even in turn crash MediaShout, because it's like the display is being hot swapped, or unplugged during use, and it wasn't really built to handle that.
I've seen the same thing happen with screens blinking and going black on a church I served at that had ProPresenter on a Mac running about 100 ft up to two TV's. They had to replace their fancy expensive HDMI cables with a converter to network cable for the distance run, then back to HDMI at the TV end, and things shaped up pretty well.
The FIRST thing I'd try if I were you is make sure you're running at no higher than 1280x720 on the Windows desktop output to the screens (not your PC monitor, that can stay whatever you want), and make sure MediaShout is matched to that in it's cue setup settings, to 1280x720. (more detailed info on www.mediashout.com/screens). That will at least be sure you aren't overwhelming the system with too much video information. Lower resolution signal can go further with less issues. If that doesn't work, I'd look at changing out the cable runs, at least maybe get something temporary and run it up there to see if it fixes the issue before running it in the ceiling, etc. Or just bring the screen back to the booth with the computer and connect with a 6 ft HDMI and see if there's a difference.