Bryan we have a slightly different date for the death of John and Hester. I'll list what I got in part from John's Civil War Pension application records in DC.
John Zull died 23 Aug. 1899 in Butler, IN his first wife Hester Smith died 6 July 1894. Don't have any further information on his second wife Ester Hayne's. Because of the similarity of first names if Hester and Ester are one in the same person?
Are you descended from Lavina or Mary?
It looks like John, Andrew and George (my wife's ancestor) were together at the Battle of Corinth during the Civil War. All of the 4 brothers were in different companies throughout the war, but companies from different states did participate in similar battles. John was with his two brothers in at least one other battle. Looks like Adam never met up with the other three as his company took part in other actions.
Do you have an obituary for John? The Butler library may be able to provided you with one. Have you gotten his probate records from the county court house? Both records often yield great family history.