Before I start, I use a base resolution of 1080p, so I've only tested it at that resolution, and in Windows 7. It should work with other resolutions, though.
I want to give all the credit to this motherfucker over here, Mr. Lolman. It's amazingly simple and it works. (It's in German, and I don't speak German, but I was able to figure it out pretty easily.)
First, make sure GPU scaling is OFF. (seems backwards, I know)
Basically, you download his little program, AMDdownsamplingGUI (aptly named) here, then open the .jar file, click "Erstellen," and you'll see:
Then change the following numbers to 2560x1440 (NOTE: In order to properly downsample the image, you have to first select 2560x1440. I'll explain a bit more below) then click "OK" to create the resolution.
Now, open up your display properties and you should have the new resolution in your list.
Clicked "Advanced settings" and uncheck this box:
or you'll get this message.
Now, select the new resolution and your desktop should scale properly. You can now start a game in 2560x1440 and it will be downsampled accordingly.
Now, if you're wanting a higher resolution, or a proper 16:9 resolution such as 2880x1620, you can repeat the steps above to create that resolution, but to get it to scale properly you must first choose 2560x1440, then from there selecting the 16:9 resolution will work.
The program was designed with 2560 in mind, from what I gather, so that's just how it works. If you choose 2880x1620 (for example) first, you'll only see a corner of your desktop as the image won't be properly scaled.
IMPORTANT: Before you shut down Windows, make sure your resolution's not higher than 2560x1440 or you'll get a black screen upon restart. If that happens, just hit F8 and boot into 640x480.
Try it out and share your experiences below. The more feedback the better.
Added new link, thanks Tess3ract
I uploaded it to another place that doesn't have ads or shitty click throughs to get it: