Per the research of Virginia Edmunds:

When his father died Dec. 30, 1878, Jesse was said to be living in Jackson Co, WI.  He operated the mill for a time, but was persuaded to mortgage it to buy a new machine.  At some point thereafter, he could not meet the payments and the company foreclosed and took the mill.  He and his family then moved into Black River Falls, and later moved to Kansas City, Missouri, where he worked for Armour and Company for many years.

Marriage documentation
 

The 1880 Census lists the following family in Albion Township, page 302D, enumerated June 18, dwelling #359:

Ed_____ [illegible], H. Jesse, white, male, 27, husb, married, Sawyer**, born WI, father born PA, mother born OH Francis R, white, female, 23, wife, married, keeping house, born IA, both parents born NY Jessee B. Edwards, white, male, 4, son, single, born WI, father born WI, mother born IA John O. Edwards, white, male, 2, son, single, born WI, father born WI, mother born IA Ole Veen, white, male, 28, boarder, single, common laborer, born Norway, both parents born Norway

In the obituary of Frances' mother, Frances was named as Mrs. Herschell Edmunds.

Virginia Edmunds' research indicates he most often was called Jesse.

These pages refer to him as Jesse Herschell, based on the suppostion that he was named for his grandfather, Jesse Hadley, and/or his uncle, Jesse Herschel Hadley.