The problem with the spacing is in fact a problem of the line around the circle. Because you work on such small scales, it determines the size of the circle! This solves it I think. In your code change the rectangle functions to
rectangle('position',[position_x + index*(diameter + distance), position_y, diameter, diameter],'curvature',[1,1],'FaceColor',[0,0,0],'LineStyle','none');
and then Jan Simon's export print(gcf, 'test.eps', '-dpsc2', '-r1200', '-noui').
After conversion to pdf, the result looks ok to me (see attached).