If the original membrane was indeed mica, that mineral is available in
various size sheets, up to 6x8 inches (around $25.00).  Those familiar
with this substance will know it can be peeled apart into a nearly
infinite number of layers, to achieve the desired thickness.

Lehman's, a hardware store which carries many products for the
non-electrified Amish, carries mica, the mineral formerly known as
isinglass, for use in stove windows.  They're on-line.

Richard Twichell