thebser, I make my shims out of brass shim stock.
It takes a little work but that is the only way I can get what I want. The cylinder shim in the photo is made from .004" shim stock. The description you gave of your barrel/cylinder gap makes me think you may need to go thicker, maybe .006" or even .008". Check your gap with a feeler gauge to see what is required. If you make a shim that is too thick it can be made thinner with the help of some fine sandpaper or a knife sharpening stone.