I can save them out in whatever format, but that won't affect the look of the descreening much.
On the 4-in-1 picture 2 trees on the background become too blurry on the pictures №3 and №4. If it's not a jpg issue, maybe it's better to provide 2 alternative backgrounds for each game: 1 descreened and 1 not?
IMO, when the image is small, the non-descreened resized one looks better, because the colors are sharper and the offset circles aren't visible on the small image. When the image is middle-sized, the descreened one looks better due to absence of these annoying circles. When the image is large, the non-descreened one looks better again, because the small elements of the image are way sharper and aren't so blurred (dunno if due to the descreening or due to the jpeg compression). But I'm not a descreening expert, maybe different descreening filters could give better results