While waiting for my PCBs, I started looking at assembling the main chart plotter.
I could fit the main components into a nice format, see the photo below:
At the top left is the Pi Zero, to the right is the video board. They're connected by two HDMI adapters, one Mini-HDMI to female HDMI, and another HDMI male-male adapter. The black Asus box is the battery powerbank. In total the components would fit underneath the display without sticking out.
I had some problems running the video through the two HDMI adapters, but the reason was that I had turned up the config_hdmi_boost parameter in /boot/config.txt, and when I removed that directive, it worked again.
As I connected the power bank to supply both the Pi Zero and the video system with power, I had a good opportunity to measure the current that the video system draws. Unfortunately, it turns out that it uses about 1.5-1.6 amps at 5 volts with the backlight on, whereas the Adafruit documentation says that it should draw 775 mA at 5V. This is a double problem - it drastically shortens battery life, and the IC on the video board gets very hot (it was almost 100 °C before I added the small heat sink), and I'll need to get rid of that heat somehow. I suspect the video board is defective, and I'm writing to Makersify that I bought it from to see if they can help. I hope I can get a replacement.