Hi! I am a descendant of John McMullen and Catharine "Katy" Basket. I strongly feel that Catharine Basket McMullen, Ann Basket ?, Jane Basket Whitaker Manuel Nichols, Elizabeth Basket Judkins, and Mary Ellen Basket Paine are all daughters of the William and Catharine Basket that are listed in the 1850 Lauderdale County Alabama Census as living on Military Road. Also, look back through the posts from David Hindman. The families seem to stay in frequent contact and often live very near to one another.
I'm afraid that I am unable to help you at this point with your connection to Henry Clay Whitaker. However, I will keep my eyes open as I continue to research this line. Also, sorry - my line does not have a family bible dating back that far.