From experience with other hobbies you might find suitable cork in an
automotive parts shop.  It is sometimes sold (in the UK, anyway) for
making gaskets and it used to be available in sheets, some quite thin,
or possibly in a model railway (railroad) shop where it is used for
track underlay, although this will probably only be in strips and one
inch or so wide.

John Farmer, UK
(Archivist, MBSGB)