My thought is that the 1731 date for Nathan's wife is incorrect and was confused w/ the Abigail Olmsted, Jabez's dau. whose b.d. was known as 1731.
In my research, I haven't seen a b.d. or age for Nathan's wife, Abigail, assigned to her during her life time. They are all done later & based on the belief that she was the dau. of Jabez. Her death date is wrapped in controversy as well. I believe it was 1833, not 1838, which was the date needed to qualify for a widow's pension. She d. in the local poor house with no chn. or family looking after her and no age recorded. In the pension application by Tilly & the Ainsworth descendants, no birth date or age is given.
There are other family births that weren't recorded in the Brookfield Town recs. that occurred there. I think that Abigail's origins remain a mystery. I am hoping that there may be something in Jeremiah's probate/estate recs., if they exist, or land deeds. I'm still looking for some proof. The search goes on. I'll post anything that I find. Thanks for your help and interest. Appreciatively, Marsha