Now I've found out that Veronica is in fact an Orthodox saint and that the Orthodox tell the same story. So, how do these two traditions co-exist? Is there supposed to have been two Mandylions?
The Orthodox St Veronica is the woman in the Gospels who was cured of the issue of blood when she touched the hem of Christ's garment. There are not two traditions in Orthodoxy concerning the Mandylion - only one, that of King Abgar being cured by the miraculous image.
Also, I know some modern Orthodox are now identifying the Shroud of Turin as being the true Mandylion in addition to being the burial cloth of Christ. I suppose this would make both the Abgar and the St. Veronica stories just folklore designed to explain the Shroud of Turin when it was held at the Hagia Sophia. Is there any evidence of this theory from former centuries?
Equating the shroud of Turin with the Mandylion is definitely a novelty, and contradicts the established traditions the Orthodox maintain about the Mandylion and its history. While some Orthodox do regard the shroud as the true burial shroud of Christ, this is not a teaching of the Orthodox Church as a whole.