Thomas Henry Morris was my great grandfather. My grandfather was their sixth child, George W. Morris. My father is James Edward Morris, George's ninth child.
In a genealogy created by one of my aunts, Wilma (Hanes) Morris, she has Martha Jane's last name spelled as "Gaghan". She did note that the Gaghan name went through a number of spelling changes over the years. She lists the earliest version from Ireland as Mac Geogheghan. This was shorten to Geoghegan when Thomas Stephen Geogheghan (born November 7, 1820 in Cock (Cork?) County, Ireland) came to America in 1837, but was also spelled as Gaghaum, Gegen, Gagan, Ghaghan, Ghoghan and Gaghan with changes in location and a new generation.
My aunt's genealogy lists more children for than you have. They are:
Still born boy, Mark Andrew & Lillie (twins), Charley, SHADRICK, KATHY (died at 1 and a half), Martha Cherokee "Mat", George W., Samuel "Sam", Myrtle.
According to my aunt, Fanny Woodson was born on July 18, 1833 in Troy, Missouri. She was one half Cherokee Indian. This could explain your trouble finding records. You may need to check the records of the Cherokee Nation. This would make Charley one eighth. Aunt Wilma wrote that she saw the list of the children in the rolls of the Cherokee Nation with their degree of Indian ancestry.