1. The best explanation of the evidence is that it is a medieval artifact
2. "the overwhelming scientific evidence to the contrary" is that put by Turinfers who disgree on their own explanations. (Much like JFK Assassinationists or UFOlogists - which actually puts them below The School of Anthropomorphic Global Warming on the credibility scale - true story)
The only reason atheists hold to this is that they assume the false dichotomy that the only explanation is forgery or miracle.
What you are apparently not taking into account, is that unlike many other bones of contention, in this case, we have an actual, physical item, rather than legend: which means that the usual skeptic methodology of "it may be a weak explanation, but it is the last man standing, and naturalistic, so it wins by default" are insufficient.
The other issue clouding this is that we don't have a hermetically sealed, forensic-quality chain of custody. Some of the folks who had the Shroud in past years tried to eliminate the image by boiling it in oil. That makes the "argument from absence" of pollen, etc. suspect -- since we don't have any way of quantifying, nor of assigning error bars, to the effects the oil had on material extrinsic to the Shroud.
If it were an image of a Roman centurion picking his nose, the skeptics would not be up in arms about it. They'd be going gaga trying to elucidate a mechanism.
Nice try, though.
Cheers!