Sharon,
Here is what I have obtained re Oakwood burials:
"Unfortunately there are no burial records showing Addicus Crockett at Oakwood, although we know that most men who died at Chimborazo were buried at Oakwood without additional records we cannot prove he is there. There are an estimated 17000 men buried and we may be lucky to identify half that number."
I would next suggest you go to the Morman Church's Family History Centers and see if they can identify Thomas Cunningham and also your man's records.
Unfortunatley, I have lost my access to Ancestry.com.
Kindest regards,
George Martin