Thank you so much for all the time and effort you've put into this.A lot of what you posted I had already come across, but some of it was new, and I'm very grateful.
My best guess is that the Helen Hawley who died in 1892 was originally Helen Reed before marrying Uriah Hawley.Her son Edgar's middle name was Reed, and the Hawley gravesite in Chicago includes all Hawleys and one John William Reed, whose date of death does not appear on the cemetery records or anywhere else that I've been able to find.
I've tried doing a census search for a Helen Reed born in New York with John William Reed as her father, but it's turned up nothing, so I'm not 100% sure that Reed was her maiden name.
I suspect that part of my problem lies in transcription errors, so the things I need aren't showing up in databases.I had this problem with Edgar's wife, the other Helen Hawley in this branch.The doctor's writing on her death certificate was misread, so she is sometimes listed as "Ellen Stanley" or "Ellen Hanley" instead of Helen Hawley.Her maiden name was Shufelt, by the way, sometimes spelled Shufeldt, and her father John H. Shufelt is another one I've been having a hard time getting anything concrete on.
I've come across some references to probate proceedings for Uriah Hawley, but I didn't know if following up on that would lead me to anything about his wife's ancestry, so I haven't pursued it yet.If you think it might be fruitful, I'll do more digging.