But this isn't really the problem. The real problem is the one of finding appropriate level of detail. At 1080 resolution, you have 1310720 pixels, respectively 327680 4-pixel quads.
Doesn't 1920 x 1080 = 2,073,600 pixels? I'm curious why you used basically half the pixels of that resolution.
I'm not a programmer by any means, so please excuse my ignorance. I'm just trying to understand your numbers in regards to pixel counts.
Hehehe, that's because I'm stupid... I multiplied some wrong numbers. You're right, it's twice as many pixels (but still the same logical consequence, even if it is not as immediately obvious).
The one obvious thing is that if you have basically as many vertices (or even more!) as you have pixels at some point. The not so obvious thing is that long before you approach that limit, you already have considerable double-shading of border fragments.
Many people use triangles instead of full-screen quads nowadays to save double-shading the fragments on the diagonal when they do post-processing. Now imagine the same thing happening with a hundred thousand small triangles all over the scene. The more triangles you have, the more pixels necessarily happen to lie on some skew line, or on a border in general, covering only one or two pixels of the 2x2 group.