I finally found James G and Susannah (Susan) WAITS and family in the 1870 Census! They're in Ohio for the 1860 census and in Nebraska by 1880. So I decided to look at every census form of anyone with a name anything like WAITS. There they were in Illinois, of all places! Pittsfield in Pike County, to be exact. Thankfully they have a really big family! They were listed with the last name of WEIT. Sweet!
My 2nd great grandfather William Henry was listed there at age 26 with his parents and brothers and sisters.
There was also an 8-month old infant named "Will", born in October 1869. I'm not sure how he fits into the family, though. In 1880, he shows up again as 10-year old Wm Mathews in Platte, Hamilton County, Nebraska living with his grandmother Susannah and her son Thomas Boyd Waits who is 22 years old and has the "Chills".
I wonder if he's Sarah Waits' son? Someone else's tree on Ancestry.com says that she passed away in 1869 at the age of 26. So it is possible that she died in childbirth. I'll have to check marriage records to see if she married someone with the last name of Mathews!
Boy, it sure helps to talk this all out here! Thanks for listening!