Just to try another idea, I added another 5 seconds or so of mouse movement to the script. The players are slower than your initial spec (even though we aren't currently doing any video on them, and only still images and 1 news feed scroll bar). They are dual core Atom's (I believe 1.6ghz) with 2 gigs of ram, running 8gb SSD drives. I've got one running windows now, and so far that I've seen, it has yet to crash. It's only these linux players that have given me issues, and as I said, they run typically 3-4 days, appear to reboot every evening at midnight, even though the program is set not to do so, and they seem to go into a blackout screensaver mode after the 3rd to 4th day that can be resolved by moving a mouse if you connect one to them.
The install is the base 10.0.4 install. Nothing has been installed in addition to the base desktop install other than the needed applications (Adobe AIR, xautomation, and the signageplayer software).