Interesting thought, wondering if AM may have lost/had stolen/or gave away a ring before she went to Ireland?It could be a relatives ring. There was an American-Irish girl called Annie McCarrick who went missing from Dublin in 1993. Although other identifiers don't match up, they have been wrong before.
The Doe Network: Case File 779DFIRL
Mentioned your post on AM's thread..
Ireland - Ireland - Annie McCarrick, 26, US citizen, Dublin, 23 March 1993