Thank you very much for all of your help. I've updated my records.
That was a typo in my post above. I meant to write "Elisha Dunham (1774-1844)", not 1884! Many apologies! I'm a little wary of those dates, as they're the exact dates also given for his wife, so I'm guessing someone may have estimated somewhere.
I'm very new to all of this (and feel a bit young, at 26, to be doing so), but I'm beginning to get myself sorted out better. The New York Public Library has a copy of Isaac W. Dunham's genealogy text covering descendants of Deacon John Dunham (written around 1907, if I remember correctly). I'm going with a friend to find it next week and see if there's anything helpful within.