I am being extra careful with “seems” and “speculated” as I don’t want to stretch the evidence farther than it goes. You want more documentary evidence on the connection with the Mandylion and the Abgar image, here you go:
“King Abgar received a cloth on which one can see not only a face but the whole body” (in Latin: [non tantum] faciei figuram sed totius corporis figuram cernere poteris)—A seventh-century account from the Codex Vossianus Latinus
“The Venetians partitioned the treasure of gold, silver and ivory, while the French did the same with the relics of saints and the most sacred of all, the linen in which our Lord Jesus Christ was wrapped after His death and before the resurrection.” Letter from Theodore Ducas Anglelos to Pope Innocent III, 1205
And some more:
* 6th Century: “The divinely wrought image which the hands of men did not form.”
* 8th Century: “The Lord (…) impressed an image of himself.”
* 9th Century: “…the city of Edessa in which there was preserved a blood stained image of the Lord, not made by hands.”
* 10th Century: “A moist secretion without pigment or painter’s art.”
* 10th Century: “The splendor has been impressed uniquely by the drops of agony sweat (…) These are truly the beauties that produced the coloring of Christ’s imprint, which has been embellished further by the drops of blood sprinkled from his own side.”
* 12th Century: “Abgar reigned as Toparch of Edessa. To him the Lord Jesus sent (…) a most precious cloth, which he wiped the sweat from his face, and on which shone the savior’s features, miraculously reproduced. This displayed to those who gazed upon the likeness and proportions of the body of the Lord.”
* 13th Century: “The story is passed down from the archives of ancient authority that the Lord prostrated himself with his entire body on the whitest linen and so by divine power there was impressed on the linen a most beautiful imprint of not only the face, but the entire body of the Lord.”
I’d really recommend you read more on this. I have plenty of experience in historical research and my nose is often buried in primary source documents from the Roman Republic on. For my part, I think the connection is pretty solid. Your mileage may vary, but it’s certainly not a case of “no evidence”.
IF any of this is actually true, all that proves is that the shroud existed in the 6th century. Some 500-600 years after Christ. Do you realize how long that is? If you traveled backwards from today that many years you could watch Columbus discover America—1492.
Presenting evidence something existed 500-600 years AFTER Christ is a long way from connecting it with Christ. The fact that they believed it was an image of Christ doesn’t mean anything.
By that time several sites had been identified that people believe to be Christ’s tomb (and there are documents from that time period showing people believed each one to be genuine.) Do those documents prove each site was actually Christ’s tomb? Of course not, because they can’t ALL actually be Christ’s tomb.
The fact that some people around 550 believed the shroud to be genuine doesn’t prove it is, any more than some people believing a specific site was Christ’s tomb PROVES it was Christ’s tomb.
There might be some evidence here that the sroud is older than 1200 (back to 550 say), but as far as it being genuine...I don’t see any. That doesn’t mean it isn’t.