Yes there is my conundrum. I too have searched the sources you mention.
The only other history I didn't mention is that the family have letters referring to 'Uncle Samuel Wilks' MD and Joseph Barber Wilks Treasurer of the East India Company. I have researched these families and can find no connection with my ancestor.
I have followed many of the Wilks family lines in Cantlow and Wimslow Warwickshire, Harborn Warwick, Newington Surrey, and others.
I found a marriage on Ancestry: 13th June 1811, Chipping Camden, Gloucester between William Watson Wilks and Mary Woodward Freeman and for a couple of reasons ( given names of parents, county, time period) feel this may be the parents of my Joseph and William but am yet to prove it.
I cannot see from my research why I wasn't convinced so will spend the next few hours looking further. You response has moved me forward again. Thankyou.