You're expecting too much from your graphics hardware. The total area of

the triangles that you are drawing covers approximately 80 million pixels
(they overlap a lot). If one uses non-overlapping triangles (with a total
area close to 60k pixels)

Ah, ok. So the problem is that I'm trying to render too many fragments, rather than too many triangles. So if I had a lot of small triangles, or a few big ones, I would be fine. However, I've got a lot of big ones, which is slow. I'll try reducing the total area of the triangles I'm rendering. Is there some benchmark or tool I could have used to figure that out? Something that would show me the time spent filling fragments vs the time spent processing triangles vs time spent uploading data to the graphics card?