Thomas Cunningham was buried at Hollywood Cemetery. However, he didn't die until 1894. Since he wasn't from Richmond, I doubt that he had a "family plot" at Hollywood prior to his death. It looks like in 1880 he lived on Main Street. I checked it out, and that address is right across the street from the current Chimborazo Park. That seems to reinforce the assumption that Addicus was buried at Oakwood.

I thank you for your help. I have a couple of avenues to look into further.