I've already gone through all that rigamarole, and in the end, if I want to use OpenGL, I basically need to turn off all hardware acceleration that I get with the restricted drivers, set the visual effects to "none" and restart the computer. Then it works much better, but in the end problems still arise from some seemingly random tiles not drawing, apparently heavily based on the water section of the map.
Anyway, it's not as if I'm actually trying to play it. I made it, I know how it ends up. For playing games, I just stick to my laptop for now, which has a much worse graphics card, but it still works for my latest addiction, Lego Indiana Jones.