This is going to take a while, as the relationships are very complicated. For example, in 1901, Salathiel and Jerusha E. (Jones) Carpenter are in Lancaster Parish, Saint John Co., NB. With them is a 'Amellia Wallis', described as a cousin. Amelia is:
Amelia Deborah Wallace b. 10JAN1874, d. 14MAR1961, m. 23MAY1901 David William McKenzie
the d/o William David and Hannah Amelia (Flewelling) Wallace. I believe it was Hannah Amelia Flewelling's brother, Frederick Dibblee Flewelling, who co-signed the marriage bond for Salathiel and Jerusha. Amelia's husband, David William McKenzie (b. ca. 1841-3) is the s/o David and Mercy (Connors) McKenzie, who had a son, Zebulon. Mercy Connors was the d/o Thomas and Mercy (Jones) Connors. Mercy Jones was the d/o John and Mercy (Hildreth) Jones; therefore Zebulon Jones' sister.
Part of the difficulty is that the Flewelling's here are descended from Thomas Flewelling, Jr. Elizabeth Flewelling, whom I believe was the second wife of Zebulon Jones, Sr., was the d/o Enos Flewelling, Thomas Flewelling, Jr.'s brother. So, while David William McKenzie would seem to have an obvious relationship to Jerusha E. (Jones) Carpenter; it is not exactly clear why Amelia Deborah Wallace (although possibly distantly related) should be a cousin to either Salathiel, Jerusha E. or (possibly) to Margaret (Dibblee) Jones, Jerusha E.'s mother (who seems to have m. 2nd a _____ Williams.) In fact, the last is likely as Hannah Amelia (Flewelling) Wallace's mother was Ann Jane Secord Dibblee, d/o Ebenezer and Elizabeth (Secord) Dibblee; and I am beginning to suspect that Ann and Margaret Dibblee were sisters; therefore Hannah Amelia Flewelling and Jerusha E. Jones would be cousins, through the Dibblee's, not through the Flewelling's.
This is only one of several complex problems I have to work through. I THINK your suspicion that James S. Jones and Jerusha, Sr. were children of Zebulon and Jerusha (Peters) Jones is very valid; particularly in the case of Jerusha (Jones) Carpenter, Sr. I'll work on the problem for a while, and send the results to you directly. I'll have to look at the Carpenter's more closely as well. Too many Archelaus' for one thing.