I'm pretty new to maya myself, so I don't know if this will work, but it's an idea. Try selecting all of your vertices (duplicates and all) and then edit mesh > merge (I think, I'm not at home so can't double check) with a very low distance tolerance (can't remember how to set that either, but there must be an option).

Maybe someone with more experience can elaborate, but the principle itself might work. Hope it helps.