I belong to the Australian branch of the Dacy family arrived in Victoria in 1851. We know that our ancestor from Ireland was one John Daicy of County Cork. Have you come across this spelling in your research? We do not know why one of his children (1st generation Australian) chose to change his surname to Dacy. It may be that he deliberately reverted to a "true" spelling or was simply exerting his independence! Any information on the Dacys or Daicys in Cork would be a great starting point to get this name business sorted out once and for all.
Cheers