In 1850 Monroe Co. Mary Wheat was living with her parents James and Lucinda and siblings.
I found the same birth notice that you found with Mary A. Wheat, Monroe Co. as mother.
In 1860 Monroe Co., M. A. Wheat is living with her parents Wm & Lucinda and siblings.
I think Mary Ann Wheat was Willis's mother.
I found the 1870 Monroe Co Census with Zachariah and Louisa Shirley as parents and Willis T. listed as a son.
The only question I have is why was Jack Shirley and Sarah E. Shirley listed as his parents on his death record? I know that this info was provided by the Informant who might not have known correctly who his parents were especially in a case like this.
I think you've drawn the correct conclusion. Successful Searching & Happy Holidays!