Holy cow, when you said lines, I thought you meant hollow shapes. Isn't it horribly slow drawing all those lines? Wouldn't it be easier to create one mesh for the whole shape instead of one per line? Perhaps there's more going on here than meets the eye, so perhaps that's not possible.
I would give it a go with floating point coordinates and see if that does the trick.
I would give it a go with floating point coordinates and see if that does the trick.