It wasn't a thousand years of silence. There are various reports of the acheiropoietos (not-made-by-hands) image of Christ throughout the period. The image of Edessa, the Mandylion, the Veronica are all echoes of the Shroud image in a frame work. that hid most of the body. This time period spanned centuries of iconoclasm where icons and images of all types were destroyed routinely. The image of Edessa/shroud was known to have been walled up in the City Portico of Edessa during the arab occupation starting about and only rediscovered after an earthquake in 525 - 544 or so after the city had returned to Christian hands. The image of Edessa remained there until it was brought to Constantinople in 944... where it was revealed to be a full figured image rather than just a face. At this time the inventory dropped the Mandylion from its listing and added The Burial Shroud of Our Lord to the list. In 1204 the city was sacked... and all of its relics were stolen, including the shroud.
You’re simply begging the question. There’s no evidence to connect those Edessa reports to the shroud, which was just of a face like the St. Veronica legend.
The Shroud of Turin has a clearly 14th century history, and was recognized as an item with only a recent history by the bishop who wrote a letter in 1389 denouncing it as a forgery. He said he had identified the man who made it, who had confessed.