1. I hate it when they get the father's name wrong on the death record.
2. I thought the marriage might be a church record, but I hadn't looked for it yet.
3. I don't think you'll find a death certif for Hannah (Fitzgerald) O'Connor. Others here might know the likelihood of an 1892 death record for New York State, but I think the chances are slim.
Are there burial records for men named O'Connor dying in that area of Co Clare? and the civil recs - except those images aren't yet on line, I don't think. Something tells me Hannah's husband died not long before they all left Ireland.
Did Hannah and Mr O'Connor have other children? Is Ann's baptism in the record? - do they have the registers that far back?
Another problem is that Hannah and Mr O'Connor were probably married in her church, not his, then settled where he was from. Her parish shouldn't be too far away, though.
"They say" that rootsireland.ie has the best index for the Catholic registers. You could try a 1 month sub and see what you find. Or try ancestry's and findmypast.ie indexes and see if Hannah & Mr O's marriage shows up, or any of the children's baptism.
also try the Co Clare forum on facebook.com. I asked them a question once about a man who died in Montana who had got a letter from Co. Clare. - That was all I knew. Within one afternoon they had his family, censuses, immigration to the US, naturalization, etc.
Oh, and have you found them all arriving? Did Hannah's husband maybe come with them? - long shot, I don't think so, but you haven't ruled it out. Any male O'Connor deaths in Woburn that would match?