Opportunity is missed by most people because it is dressed in overalls and looks like work. - Thomas Edison
I always thought ellipse was used in order to prevent moire.
Tossing in the added variables of aligning "different' screen angles hoping that you don't get any moire is just compounding your potential problems.
I think you'll agree that using a single angle is OK, but get one of the screens slightly misaligned and the moire is horrible.
A line screen as opposed to a halftone dot, does not moire.
It doesn't mean that lines can't moire - drive on a motorway with a pair of fences beside and you can see lots of moire, but there are twice as many angles that won't moire.