Force app to fit on screen
After googling for a while I found a solution. Enable adb debugging on the phone and run this command:

adb shell dumpsys display | grep mBaseDisplayInfo


Find the part that says "density". This is the screen DPI. Reducing it will make Android think your screen is bigger, and it will shrink all of the UI respectively. I changed it from 240 to 200 by running this command:

adb shell wm density 200


Now the problem app looks like this, and I can use it:


screenshot showing fixed app

Note that this will affect everything on the phone including the homescreen.

I found this solution here. Contrary to what that page says, I did not need to reboot for the change to take effect.