I enclose a picture, you see that my prototype was high level science, lol. Simply bend a cord at the lid hole and the hole in the moving servo arm, where normally the rod is fixed, no big Thing.
As Scott explains, the thickness of the lid plastic together with the benting of the metal rod at the top leads to a moving/turning side pressure of the rod when teh lid opens. You can feel that when you push the rod down with your hand when the rod is not fixed at the servo. Due to the fixing of the rod, the turning movement is transferred to the top, which leads to a rough opening movement of the lid. The other disadvantage is that there is permanent pressure on the servo and the arm.
A cord avoids this pressure on servo/arm. However, my "prototype" Installation does not move smoothly, which seems to be due to the movement of the metal stick during the opening process. I think the crucial point is how to realize a smooth travel of the cord in the lid plastic whole during the opening. My next approach would be to use a metal washer with a pearl on top (see picture), just an idea. Very easy to install and the pearl moving during the opening might lead to a smooth opening, I will see. But everybody can test as well or contribute other ideas in this regard.IMG_3557 (resized).JPGIMG_3561 (resized).JPG