Michael-- Michael H Hawley (1856 or 1859-1940) was born in Neenah (per marriage record, but can't find Michael's birth record; I do have the actual birth records for a few of Michael's siblings who were born in Little Chute, Outagamie, WI).
Michael married Annie Ellsworth Devine in 1883 in Lebanon, Waupaca, WI (familysearch.org)-- NOT Neenah, WI as you say.
They moved to Minneapolis, MN by at least 1895 (city directories).
According to Timothy's obit and death certificate (Michael's father), Timothy was born in County Clare, IRE, but that is yet to be confirmed.
If we follow Irish naming traditions, the first born is named after the father's father. In that case, Timothy's first born, John, may have been named after Timothy's father, so that would make Timothy's father's name John (NOT Michael). Again, that is supposition.
I guess, I am just saying that your thoughts are just suppositions, until we get further data to support one way or another. Thank you.