Johanna, Tatsume, Ilaria and Teleri attending this one.
Teleri was inspired by Magistra Ragnveig's Facebook posts on her period hike, during which she used waxed linen to keep her lunch dry and fresh. We proceeded with the project sans authentication, because plausibly-period tin foil replacer sounded like a good idea. (Teleri in particular got bug bits in her water pitcher at Ruby Joust, and wanted a cover for it.) A quick Google just turned up a reference to waxed linen in "a Norwegian regulation", no date given, but the context of the paragraph seems to be late medieval.
We melted beeswax in an improvised double boiler - foil over a steamer insert in a 3-qt pot. It worked, but eventually wax got everywhere.
We cut small rounds of linen and easily dipped them entirely in the wax. The excess dripped off, and we got very strongly waxed rounds, suitable as cup or pitcher covers.
We also tried a large sheet of linen, maybe 18" square or so. Tatsume had some experience with Japanese cloth wrappers, and thought this was about as small as one would want to go for a lunch-sized package. This did not work so well in the small pot despite Meisterin Johanna's best efforts. We dipped corners, we tried pouring wax on it. About half got well-waxed, and about half was either unwaxed or had wax sitting on the surface but not really penetrating the fibers. Her Excellency Ilaria (if I remember rightly) Googled up a technique that suggested pressing the linen between sheets of parchment paper with a hot iron.
A few days later, Teleri attempted the iron trick solo. It actually worked very well, with a caveat. There was a lot of extra wax. Once it melted, pressing it with an iron sent it flowing out to the edges of the parchment paper. Wax got on the ironing board cover (will likely need a new one), the carpet, and Teleri. But the linen is pretty well waxed now.