The 14th century theorem has long been debunked, as the Pray-codex https://en.m.wikipedia.org/wiki/Pray_Codex contains strong evidence that the shroud was already known in the 12th century.
IMO a plausible theory here is that imagery of Jesus's death with those "distinctive features" was already popular at the time and both artifacts are representative of that imagery.
Besides that, I wasn't aware of this codex, so I'm glad you shared it. Has anyone suggested that (assuming there is a relationship) the arrow of causality might go the other way? That perhaps this image was a reference for the shroud itself?