Hello, Brian,
Your family and mine probably do not intersect, but I live just outside of Eagarville, Illinois 62023, which was named for the English-origin farmer -- John Eagar -- whose farm provided the site. This property is located in Macoupin County Illinois and the county records are kept in the courthouse in Carlinville, Illinois 62626.
Coincidentally, a few summers ago I encountered an older man from Arizona who was driving across country and noticed the Eagarville name on the map. His last name was Eagar and he mentioned relatives on the east coast and in Oregon. He seemed to know a lot about the Oregon family's trek west. I believe he lives in an Arizona town with the word "Eagar" in it. He said his town is much larger than ours (we have only about 72 residents and no businesses or services).
I'm sorry that I don't remember his first name or the exact name of the town, but I hope that this provides a productive lead