The standard "neutral" way of setting up drop bars and levers is to place a ruler along the underside of the drops (so it sticks out forwards) and adjust the position of the levers so that the tip of the lever just touches the ruler or is a bit above it. Then rotate the bar so that the ramps are level i.e., parallel to the ground, or form a straight line with the stem (which is often roughly level for a quill stem like yours). Some people achieve much the same by pointing the drops at the rear hub.
Your bars look like they're rotated too far forward, so I'd agree that you need to rotate them backwards or, as you said with reference to your picture, clockwise. I did this and it made getting onto the hoods much more comfy.
Old non-aero levers like yours only really work well from the hooks (your position 4) so not being comfy in this position is bad news. I'd highly recommend upgrading to modern aero levers as you get much better braking from the hoods. These are nice and look quite retro or, if you've got big hands and don't mind a more modern look, these or these.
Awesome article!