You are assuming a usage for the face cloth that was not how it was used. With a Shroud, a separate face cloth would have been superfluous. Instead the cloth that had covered his head after death on the cross, was rolled into a kerchief like form and used to bind his jaw AROUND the face... not over the face. The Greek word works either way... but the Jewish instruction for burial works only one way and the mouth needs to be kept shut.
But your cohorts claim there is an identical facial image on the 'original' facecloth as on the shroud...It's gettin' harder to know which spin to disbelieve the most...