I believe John died shortly after Mary, assuming she died in 1783. I have his death as 29 November 1783 Bisbrooke, Rutlandshire, England. However, I don't have actual records, just an index. Why do you think the 1783 death is someone else?
Kezia Woodward Steel and possibly her brother James Woodward are the only two children found near Cubbington. I believe Mary's Allin Woodward's burial was 22 Mar 1816 Uppingham, Rutlandshire, England. Once again, only going from an index. If you read the post before, you'll see I was mistaken and mixed families. Her youngest child would have been 6 at the time of her death. The oldest and youngest child are found in Uppington. William is found in Flecknoe, however, it isn't clear if he's really Kezia's brother as the naming pattern is way off. The 1843 death can't be his as he's found up until the 1881 Census.
I do have the elder William Woodward attached to the census you mention, but didn't have the death date. It makes sense that he was living near his son, if the younger William is his son. We should probably flip pages and see how close they are to each other in the census.
I cannot find any of the other children. I wonder if the children became a burden on the parish and were farmed out to relatives or as servants. However, I have no idea how to search the poorhouse records to see if the children or William was there. In the 1841 census William is listed as a Ag laborer, but we don't know if that was his occupation or just due to his age. Perhaps a view at the actual marriage record, or the children's christening records would give us more insight, especially if they list an occupation.