I know several girls of Indian descent called
Mira (or
Meera) said MEE-ra. I can't imagine anyone saying
Mira like MIE-ra.
Myra makes much more sense.
This might just be a UK thing though, but naming a child
Myra is asking for trouble because of
Myra Hindley
http://en.wikipedia.org/wiki/Myra_Hindley, it's like a forbidden name, but I have no idea what reactions would occur elsewhere - so this is just my point of view.
Elmira is beautiful. She could go by
Ella or
Mira :)