Another great post! This would seem to clinch the argument, wouldn't it? Now, all they need would be to repeat it a couple of times, and the debate would be over -- or at least drastically recast!
Of course, from the Church's perspective, why end the debate too quickly? Why not let new ideas percolate and soak in slowly, so to speak?
For certain, the Shroud has a most interesting history, which will have left many different marks and deposits on it. Look at one section and it says: Medieval repairs, another section may say: sixth century Byzantine, still another: first century Jerusalem, who knows? Perhaps fully unraveling all the Shroud's mysteries could take as long as the Shroud's history itself?
The KEY word is "unauthorized" and the results cannot be published although they are talked about among Shroud investigators. The Church did not authorize the C14 test on one of the threads taken in 1978 but it was done. The results strongly suggest that the main body is first century. With modern C14 small sample methodology and accuracy, a few 1 cm threads would be sufficient for numerous tests.