It's not entirely orthogonal. John's name appears as 4th son in his father's Visitation pedigree, but that's the only record of his existence. If he's going to be used to connect immigrants to the astronomer, he has to be beefed up a bit, to counter the impression that he probably died young.
There was a previous thread. From memory, there was an article in the NEHGR, 1860s, which made some dubious claims based on alleged family papers. Editorial standards were low then. It was challenged in a later article by Osgood Field.
Joseph Foster did a big chart pedigree in his 1875 Yorkshire Pedigrees book, based on Osgood Field's work.
Sadly for Foster, Osgood Field continued his research, and when he published his own book in 1895, some things had changed.
FC Pierce (best known for Richard Pierce of Pierce Hall and other fabrications) put out the Big Book of Fields in 1901, 2 volumes. The English end mostly follows the 1895 book (and shamelessly plagiarizes it), but makes some adjustments in favour of the immigrants.