Now the serious part: does there exist a map of what-was-taken-from-where-when?
Somewhat. Since the inception of scientific examination, records have been kept. The worst of this "scientific" examinations occurred in the secret "restoration" in which uninformed restorers, in an attempt to put out the fire of 1532 (someone told them that the charred areas could still be expanding), snipped away all of the charred edges and "vacuumed" the rest of the shroud for contamination, and put the results in plastic baggies according to defined zones - which destroyed any in situ evidence that could have been garnered in the future.