Short version:
Running a game in windowed mode and using
SRWE to resize your window to a much larger resolution for screenshots.
This allows you to play at any resolution you're comfortable with (for example, 1920x1080). Then when you're ready to take a screenshot, you swap to a much higher resolution with the same aspect ratio (like 5120x2880). In that case, the window will be so large that it won't fit on your screen, but a screenshot will still capture the whole frame. After capturing a show, you can resize the window back down and resume playing.
Then you can downsample the images for aliasing-free screenshots.
Here's a crappy one I took of GTAV downsampled from ~24 megapixels.