That would be an excellent argument except for one obscure bit of forensic trivia. If there is enough bilirubin in blood it stays red forever! Its medically uncommon to achieve the needed level of bilirubin so our expectation is blood will turn dark. However, the kind of torture both the shroud image and the gospel stories report can produce that level and bilirubin has been identified in the shroud stains.
So this actually is one more argument against forgery. It is unlikely that any prospective forger in the hypothesized time frame would have known this trivia. So the best possible forgery then would have featured the 'expected' dark, not the observed red, blood stains.
Thanks, good to know.