I would suggest removing the screw and after cleaning the threads apply some blue Locktite to the threads and replace, tightening to where it is clocked. The blue Locktite is not permanent so the screw can be removed. I have little faith in the shim method. Under the head it might raise the screw enough to interfere with the closing of the top lever.

When an old man dies a library burns to the ground. (Old African proverb)