I am a Gainan from Montana, actually I married a Gainan. I have been doing research myself and this is what I have found. Stephen Joseph Gainan came to Montana from Iowa, but was born in Pennsylvania. He was quite the war hero. His dad was James Gainan from Limerick Ireland, and his mother was Catherine Burke who both passed away in Penns. I attached a pedigree chart of my husbands father.
I have had the same problem as you with the last name of Gainan, not sure if it was changed when they came here, or what. If you find a connection please let me know.