John Wallis 1777-1858 of Sanbornton, N.H.

When trying to re-assemble the family of Nathaniel⁵ (Samuel⁴ William^3-2 George¹) Wallis, I noted that his entry in the 1790 census had two men over 16, 6 boys under 16 and three women.  Generally, although not certainly, it meant that his household consisted of himself, his wife Deborah, seven sons and two girls.  I can account for five males via the Moultonborough marriage records; one daughter via the same way; another daughter via deeds.  Certainly two of the sons may have died young or married elsewhere.  Based on the good advice of a commenter to this posting, I have removed both John and James Wallis from contention as sons of Nathaniel⁵.  Curiously this leaves Nathaniel open to serving in the American Revolution, which I've often thought he must, but sadly he leaves no pensions records that might help in assembling his family.

John Wallis has an entry in the History of  Sanbornton by M.T. Runnels (1881), II:825.   His birth year is based on his age at death (81 on 26 September 1858).  He married for the first time on 5 January 1804 and that holds with a 1777 birth as well.  Runnels gives his line as John⁴ William^3-2.  That's off by several generations.  Assuming Mr. Rand is correct and that John comes from the Pittsfield Wallis family, that family is William⁵ (William⁴ Samuel³ William²). According to Rockingham Deeds 104:72, William Wallis of Nottingham, N.H., yeoman and Mary his wife, sell to Samuel Wallis of Newcastle, house carpenter, 25 acres in Epsom that his late honoured grandfather Samuel Wallis, deceased, had of William Seavey, 101 in 3rd range.  dated 2 January 1771 and recorded 19 March 1772.  

So, as we can see Runnels gets the descent wrong.  Everything else about the sketch may well be true.  I liked this guy because he's (i) born at the right time; (ii) has a name not already accounted for in the Nathaniel family; (iii) named his eldest son Samuel.  Of course the last thing works for either side of the family.  Sanbornton isn't too far from Sandwich were Samuel⁴, father of Nathaniel⁵ died.  So when I'm trying to piece together people, this is basically the way I work.  What commonalities do they have that might distinguish them and place them into their proper families?