The thing I figured out here is that you need the dots to be 3 pixels in radius to hover over them, and that it doesn’t matter how wide the line is – the cursor will pick up the dots anyway. So make the line 6 pixels and you can hide the dots. Ta and dann.
Also, gridlines. Again, nicked from the Tips and Tricks book. I just needed to figure out how to move them up and down, which wasn’t too tricky. The effect is good, though.