If you're dedicated, I think it's possible to fake parchment/papyrus/ink/whatever from any era you like.
Build a reasonably-airtight greenhouse. Flush it, not with regular air, but with CO2 from an coal-furnace exhaust. That's pure 12C, no 14C, and will appear too-old-to-measure in a spectrometer. Grow a supply of plants in this greenhouse; now you've got 14C-depleted plant material (paper, papyrus?). Raise a goat for a few years on a strict diet of 14-C-depleted plants and you've got raw materials for fake "old" parchment.
Oak galls might be a challenge.