Is there a way to set your monitor to any arbitrary resolution and aspect ratio (like 1000x400, etc.)?

"Entech Taiwan makes a product, PowerStrip (sharewhare), that does that. Or else you can try manually editing your registry, like these directions show. (I've not tried that personally, so where knows if it will work).

Although you could just set your application's window so it always opens to 1366x768 for testing."

You might be able to do it by going to Display Properties, Advanced, Monitor Tab, and uncheck the "Hide modes that this monitor cannot display". This will let you choose some other options for the resolution.