If you want cork to have stable thickness (for accuracy in a mechanism), then natural cork is pretty hopeless, especially if it is over 0.4 mm thick. For these situations, I (along with Yamaha and Yanagisawa, but not Selmer in their apparent ignorance) use a composite cork such as what Musicmedic sells. It is far more difficult to sand this to a different thickness, although it is available in a wide variety of thickneses. Here is where adjustment by bending (of metal parts) comes to the fore, and is standard practice, both in manufacture and susequently. Of course, you need to know what to bend, how to do it safely, have appropriate tools, and be able to deal with any problems this may create, such as a binding pivot. This is where a good technician is invaluable.