OHio started recording deaths in 1867. Early death records are at the Ohio State Archives.
You won't find a real obituary because they weren't used until the 1900s. You found the newspaper death notice which was all that was published (unless the person was famous) in the 1800s.
I doubt you'll find his funeral home records because a funeral homemight not have been used. Also if the family did use a funeral home, the records could have been destroyed or anywhere by now.
Finding the Reverend's records also will be next to impossible.
The Ohio Archives should have Patrick's probate records. Successful Searching!