Illustrator :: How To Make Smallest Increment When Moving Object

I'm working in a file zoomed fully to 6400%. I've changed the Keyboard increment to the smallest it will allow to 0.0036 mm.
 
I have two lines. Line 2 sits on line 1, a fraction above. When I select line 2 and press the down arrow key, it jumps so that line 2 is now a fraction below line one. I cannot get the lines to sit perfectly onto of one another.
 
I have tried to move the line using the mouse, but it snaps to the same position as the keyboard press.
 
I have turn off snap to grid, snap to point, all the guides, smart guides.