Well, that didn't work too well, but I did find a workaround. An answer to an earlier post directed me to the folder "C:\Users\<username>\AppData\Roaming\UFOAI\2.5\base" for adding scripts and modifying video displays.
After a few rusty gears in my head started turning, I had an idea. I extracted the maps folder from C:\Program Files (x86)\UFOAI-2.5\base\0maps into C:\Users\<username>\AppData\Roaming\UFOAI\2.5\base and voila. Happy program.
For whatever weird reason, it seems like Windows 10 likes working with the AppData folder more than the Program Files folders, so this worked for me. Everyone else's mileage may vary, but here's another option.