Aha, I get it now.
My primary monitor is running at 720p. So the second display has to run at that aspect ratio as well. So since my second display is 1280x390, I need to scale up my image height by 1.85 for them to look right.
When I did that, it looks good. It doesn’t fill up the entire display, I’m not sure why. But at least it looks much better.
Now I just need to automate the whole thing somehow.