Ok, I built another one.
DIYPC ATX case, RGB LED rear fan, RGB LED vertical strips down the front, pretty bling-y. Tempered glass side-panel too.
https://www.newegg.com/Product/Product.aspx?Item=N82E16811353157&ignorebbr=1
MSI B350 Bazooka micro-ATX AM4 mobo
Athlon 200GE AM4 APU
Corsair Vengeance LPX 2x4GB DDR4-2667 kit (Black)
Patriot "Scorch" 256GB M.2 PCI-E x2 NVMe SSD
SeaSonic S12II 520W ATX PSU (80Plus Bronze, 5-year warranty, I think, maybe just 3.)
Overclocked to 1.40V, 3.80Ghz (38.0 multi) in BIOS.
Installed Win10 64-bit Pro 1809 (while overclocked). Installed AMD driver 19.1.1, and before that, newest Chipset drivers for B350.
Guess what? No weird "static screens" over the HDMI.
I'm wondering now, if I had overclocked the previous A200GE MSI OC Win10 box to 3.90Ghz before I installed the AMD drivers? Because, Linux Mint 19.1 wouldn't install at 3.90Ghz, it would hard-freeze, I had to clock it back down to 3.80Ghz.
I'm going to re-install Win10 on the first box, at 3.80Ghz, and try again.
Edit: No go. I used a Win10 USB to re-format the main partition and re-install to it, then I followed the procedure that I followed with the "working" (no static) system, but... this rig still has 7 screens of static before it settles down. It's not an HDMI cable issue, it's not a display issue, it doesn't appear to affect Linux Mint 19.1 at all, just the Windows' drivers, and just that particular rig. The mobo doesn't want to re-start properly either. Have to power-off and power-on to reboot to access BIOS, or re-start Windows 10. I'm pretty sure I disabled Fast Startup in Win10. Maybe the PSU is bad? It's pretty-much new, but it's a Rosewill. Works in Linux fine though. Maybe I'll try re-flashing the firmware on the mobo.