Eugene R. Wooster gives the same ascendancy for John Benjamin Wooster as does Donald Lines Jacobus. This, however, is not surprising, as it seems that Eugene R. Wooster used Donald Lines Jacobus as the basis for his work, turning only to David Wooster and others when additional material was needed. (BTW, I think you made a typo and assigned Mary Walker as wife to the wrong Abraham in the David Wooster version of the ascendancy. My interpretation of page 15 of David Wooster is that she was wife of the second generation Abraham.)
Since Donald Lines Jacobus was a professional genealogist and since he seems to have consulted many more official records, I think there is little question that his is the correct version. Jacobus says that the Abraham given by David Wooster in the third generation was fictitious.
An error that David Wooster seems to have made concerns which of the first cousins of the father of 4th generation Edward Woosterwas Edward's guardian. David Wooster says on page 28 that he was adopted by David (the General). Jacobus cites probate records on page 185 (or page 11, depending on version you have) that Edward chose Capt. Joseph Wooster as his guardian.
Captain Joseph and General David were brothers. It seems to me that the author David Wooster did not understand that these two brothers were first cousins of and not the brother of the father of the 4th generation Edward. It seems that this misunderstanding led him to create an Abraham in the third generation as an older brother of Capt. Joseph and Gen. David in order to fill the gap and provide a father for 4th generation Edward.
You also asked if I know the parents of Lydia Stuart. The answer is "no."
The connection to the White Star Line is fascinating. Like a lot of other people I love the lore of old ships.