It now appears like we've pretty thoroughly nailed down the family of Jacob Wood . This family has been entirely assembled using autosomal DNA matches of mine, found in FamilyTreeDNA, based on three specific sections of DNA. Note that I still am pursuing a bunch of matches that go through the son named "Joseph?", who lived in either Sussex County, NJ, or Bergen County, NJ, and has now two known children, and I am sure there will be more surprises. But now, if you look at the timeline, you can see it has become pretty crisp.
There are only very few records for this family, which I have no good explanation for, other than a speculation mentioned below. Suffice it to say that it has taken many months to put things together enough to present.
Let's start with what we know from records.
* Johanna Daniels' father Jonathan left a detailed will mentioning daughter Johanna Wood. The will was written in 1764 in Woodbridge, NJ. In it, Johanna was granted 20 pounds sterling, the most of any family member mentioned.
* There was a marriage recorded in Middlesex County, NJ, between a Mary Wood and a Paton Parmer, dated 1763. In the record, both Mary and Paton were said to be from Staten Island.
* Many children of Jonathan Daniels accompanied him and his wife Mary Potts to Woodbridge.
* Other children of Jonathan Daniels, at least three of them, eventually left the Woodbridge area and went south to Bedford County, Pennsylvania, where they stayed for many years. Several grandchildren married with families such as the Mellotts and the Pitmans and the Palmers there.
* [https://books.google.com/books?id=-cCWiUBMSvQC&pg=PA331&lpg... Staten Island baptism records] mention several children of a Stephen Wood, who apparently lived on Staten Island for most of his life.
The marriage of Mary Wood tells us that the Wood family lived on Staten Island at least until 1763. Staten Island is right across the river from Woodbridge, so there is a location affinity there. But, more interestingly, the records referenced above demonstrate that there was a Daniels living there starting as early as 1719: Margaret Daniels. This is a heretofore unknown person who recorded several children born on Staten Island. She was likely a sister of Jonathan Daniels who had gone south with one of Jonathan's brothers, who wound up in Piscataway, NJ. It is therefore plausible that Johanna wound up living with her aunt before she married on Staten Island. It makes sense, then, that she would have married a Wood who was a Staten Island Wood - which would mean a son of Stephen Wood.
DNA allowed me to fill in Johanna Daniel's children. Captain John Wood was actually already well known and had fought in the Revolutionary War before eventually emigrating to Leeds County, Ontario, Canada via Claverack, New York, and points northwest of that. I have four or five DNA matches from his descendants overlapping the right part of my DNA to be clearly Wood family DNA, which places John as the first-born son of Johanna Daniels and Mr. Wood.
I also have several matches who are the descendants of John Noah Mellott, son of Theodorus Mellott and Amelia, "daughter of Jacob". It seems clear that Amelia is really Amelia Wood. This hints that her father was Jacob Wood, and since she must have married in Bedford County, PA, it also is a strong indication that the Wood family left Staten Island at some point for Bedford County, like several of Johanna's sisters and brothers. I originally thought Jacob was called Joseph based on a web tree - but it turns out that father Stephen Wood actually had a later son by that name, so Jacob it is.
I will try to summarize the rest of the children of Jacob and Johanna as time permits later in this discussion, and how I located the ones who weren't named explicitly in trees as we knew them. The two hints that are dead giveaways are: (a) Bedford County, PA, and (b) twins. Johanna's family had a set of twins, and almost every daughter Johanna had also had a set of twins or a daughter with a set of twins. For example, I wound up moving Hannah Islestine from the daughter of Benajah Daniels because her only known daughter had had twins.
I still don't fully understand how come Jacob's family left so few records behind. They clearly were heavy bible readers based on the names alone. One interesting possibility is that they were dabbling in Quakerdom - note that Martha Wood married Freeman Roberds, who also dabbled in Quakerdom and went so far as to head to South Carolina as part of a Quaker group.