Not sure that you are still working on the family of William Mitchell & his wife Mary Margaret Stewart. This is about William/Mary, part of my Mitchell family.
My great Uncle, Rev. George Washington Mitchell, told me many years ago before his death at almost 101: Bill the brother of his g gf John Mitchell, Jr., "..was said to have left Cheap Hill and moved across the Columbia River near Bellsburg." That location puts his moving to Dickson Co., TN.
Family tradition is that the Mitchell's & my Walker's were among the earliest settlers in Robertson Co., TN, in the area that became Cheatham Co., TN.
The 1820 census for William Mitchel showed the following: Springfield, Robertson Co., TN: 1 0 0 0 1- 1 0 2 (young male would be William Milton b 1817; young female was Elizabeth [m Aaron Pinson]b 2 Apr 1815).
I assume that the William's wife was indexed wrong or a wife had died & he had help with the children - Mary Margaret Stewart 1792-1865 is confirmed in the 1830 census.
One of William's close neighbors was my ancestor Sterling Shearin, next door to his s-i-l my ancestor Hardridge Walker (Jr.), who lived in West Robertson Co., TN, in the area that became Cheatham Co., TN.
The 1830 census of Dickson Co., TN showed William Mitchell: 101001 (30-40)-311001. The 1840 census of Dickson Co., TN showed William Mitchell: 1010001 (40-50)- 0102101. (I believe that William & John, Jr.,had brother named Samuel, plus others.)
W. Ray Walker