I can't confirm that the James Gregory family moved to Huron County because he inherited a farm from his aunt, but I can provide some additional dates for the family.
I went into the book of cemetery inscriptions for Huron County, and found the Banta and Gregory families buried side by side in Riverside Cemetery, in Monroeville Ohio.
Section E - Row 26 plot 51 Isaac Banta, died May 26, 1888, age 74y 7m 20d George W, died March 27,1869, age 23y 26d Frankie L, s/o GW & R Banta, died April 21,1869, age 1y 2m 14d R, 1848 - 1911 G W, 1869 - 1907
plot 52 Belle Snider Gregory, 1874 - 1951 James D Gregory, 1867 - 1939
I was able to access the Death Certificates for Rosamund Banta and Belle Gregory. I couldn't find a death record for James Gregory.
Rosamund Banta died Sept 29, 1911 in Ridgefield Township Huron County. She was buried in Riverside Cemetery, and is undoubtedly the R, 1848 - 1911 buried in plot 51. He death certificate lists her parents as Tunard Dickerson (may be Dickinson), and Mary A. Platt, both born in England.
Belle Gregory died January 31, 1951 in Cleveland, Ohio. Her death certificate indicates that she was living in Lakewood, Ohio (a suburb of Cleveland). She was apparently living with one of her sons, and had been living with him for 17 years. She was born October 27, 1875 in Canada. Her parents are listed as Peter R. Snider and Sarah McIntosh. She was buried in Riverside Cemetery next to her husband. By the way, the index for the Huron County Cemetery Inscriptions has an error. As you noted it lists a Belle Snider Banta in the index on page 769. If you go to that page, you find Belle Snider Gregory. Someone made a transcription error -- ther is no Belle Snider Banta.
Her death notice was published in the Cleveland Newspaper on February 2nd. The Cleveland Public Library has these death notices on line at: