Since you know when and where Fred died, you can obtain a copy of his death certificate, which should show the names of his parents.
Once you have his father's name, you can look for the family on census records, and pick up names of the brothers.
Have you looked for an obit for Claude, survivors are usually listed, and it might give relationship of Fred to Claude in the obit.
You might check the 1900 census for John R. Wood, wife and Claude should be about 3 yrs old.See where they're living, any where near other members of the family?
I would check the Jefferson Co, TX, and Newton Co, TX GenWeb sites, some GenWeb counties are putting their cemeteries online.There must be a reason why services were in one county and he was taken to be buried in nearby county.Could be his parents or other family were buried in Burkeville.
I wasgoing over your query again, when I noticed something about the dates.Fred was responsible for bill of Claude, born 1897, age 50 yrs old.Wouldn't that make death date 1947?You say Fred died 1939.
Now, if 1897 is date of death, then Claude would have been born about 1847, and that would make him old enough to be father of Fred.If that is the case, I really would get a copy of Fred's death certificate, because it would say if Claude was his father, then from funeral info, you would also have Fred's grandparents, John and Savanah.I'm keeping my fingers crossed. (^_^)