Hi there,
This is Bogdan from Romania.
I'm a mechanical engineer - specialized in the industrial robotic field, 3D designer and modeler (from time to time and some projects I could make the functional prototype too).
I'm doing product design, industrial design, reverse engineering, ideation, etc.
I have over 15 years experience working on various systems/devices across multiple industries, from concept to launch.
1 - the entire cork block should be made from small elements glued together and treated with a sealant in order to prevent moisture absorption (i worked with cork - for some furniture products, and if the cork is not treated will have issues...) - i could point you in the right directions where to buy cork blocks with the desired dimensions, or close...
2 - while your design looks pretty well defined, it will be necessary to adjust some features in order to allow the milling bits to carve the block
3 - you will need a minimum 3 axis cnc router, but this will be justified only by a large quantity/order.. - for the prototype, i'm recommending classical methods...
4 - if you'll use classical methods (cut and grind) will need some checking patterns...
Regards
Bogdan