I think I might be the Claire in question. As I remember, the California Toynbee family that I chatted with is from the same branch of our family tree as Polly Toynbee's.
Polly is descended from the George Toynbee who was born in Waddington in 1783, and farmed at Heckington. One of 11 children himself, this George was married twice (to Elizabeth Cullen, then Sarah Obbinson) and had 15 children.
The Charles Toynbee who married Elizabeth Snow was this George's younger brother, born in 1786. Their parents were the George Toynbee who was born in Waddington in 1749, and Sarah Starkey.
Are you sure of the connection to Frances Burrell? She doesn't seem to appear in Jacky Clark's Lincolnshire and Fenland Families tree -- was she perhaps a second wife?
Have you ever run into anybody named Taughenbaugh or Taughinbaugh? When I search at FamilySearch.org without exact spelling, it comes up with that surname in Pennsylvania.
Claire
Canada
PS: The direct URL for Jacky Clark's family tree is
http://www.linclinks.co.uk/