It's inefficient, but you could also try replacing every line with a quad (made of 2 triangles) placed/shaped exactly as you want.
The triangle-covers-pixel/sample tests are very well defined, so it should work the same on every device/driver.
Interesting, I didn't think you could draw a single pixel thick quad. I tried it and it seems to be working perfectly.
I had an idea last night that I'd like to try first before committing to that option: Is there an easy way to detect what kind of card is being used? That way I can just modify the code to do one thing for NVIDIA cards and another for AMD or whatever else that is different.
EDIT: Never mind that last part. I just tried on a computer with integrated Intel chips and the only thing that looks correct is creating a quad so I think I'm going to go with that solution. Thanks a lot Hodgman