Just a thought before you go further. Is the lid actually fitted tight onto the hinges, it simply pushes on? If there is a gap on the tabs at the end of the hinges then it needs gently but firmly pushing home until the tabs at the hinge ends are properly in place.
If it is an adjustment problem with the left hand side you need to bear in mind that this could affect the CD playback. Turning this screw will also have an affect on the "lid closed" circuit as the whole of the left hand hinge assembly (where this switch is located) is moved. It also affects the vertical aspect of the lid so a bit of trial and error may be called for. The adjuster in question simply moves a cam assembly so you can keep going round in circles and eventually get back to the original start point. If only minor adjustment is needed then half to 1 full clockwise turn should do the trick.
BTW - have you checked that the left hand hinge is OK? If the pivot point has cracked then this could also be causing the problem as any small defect there has a knock on affect which is amplified through this quite complex assembly.
Chris.
The use of metaphors should be avoided like the plague. They're like a red rag to a bull to me.