Finally another Debian user!
I ran into this problem with Debian 9 LXDE on my CF-19 MK4. The screen would sometimes suddenly display total garbage, go black or a combination of both. I worked around it since it was originally dist-upgraded over Debian 8 and still had a few kernel 3's. I just reconfigured grub to load the latest 3.16 instead of kernel 4.x.That seems to have isolated the issue and hasn't crashed since.
I haven't really had time to research the issue and figure out if it is a known bug that is being worked on.
What's the full model number of your CF-31?
It's a CF-31ACAAX1M, i was very tempted to install Jessie and then dist-upgrade to Stretch keeping the older kernels but now that i have everything working i don't want to break everything until i'm quite sure what the problem is. It's likely to be a kernel firmware/driver for the integrated graphics but i dunno for sure. What you said about the kernel is quite a bit of information and i would add that the issue poups up very fast when messing around with the windows (window manager) in KDE plasma 5. In Debian 8 Jessie i just installed LXDE because KDE plasma 4 does not honor the Dvorak keyboard layout for various applications, LXDE (GTK) does. That issue is solved in plasma 5 but the system crashes would turn the laptop unusable, so, maybe i'll try the thing with the kernel, but i have to digg a bit more because many apps wouldn't be able to build kernel modules, like Virtualbox that i use very often.
I'll post any updates!
I leave you with my Dvorak layout keyboard (with stickers that partially glow in the dark because the backlit underneath)