I believe that I have the same 'old' file which you reference, showing that Parnell Pickett (1758) was the child of Ebenezer and Parnell and the father of Rev. Daniel. It included the names of four sons of Daniel and Anna and reported that Anna died in 1812, before her children were born. Another problem is that Parnell Pickett (1858) was female and married James Hawley in 1779.
Also, the 'Notes Ependatory' to the Case biop does not say that Rev Daniel's parents MOVED to Canada though that is the implication. These notes have gross errors about Rev Dan marrying E F Ingersoll in the 1790's when he was in his 'early twenties' when, in fact, Ingersoll was his second wife who he married in his mid thirties.
The notes from Dan's g-grandson, Betherl S. Pickett, clearly state that Dan grew up in New England, as opposed to the 'home grown' Canadian statements.
As stated before, the facts surrounding Rev Dan are confusing and contradictory. No one source is complete and beyond challenge.
Similarly, whileno histories of the Bostwicks and Wheelers include Rev Dan with the nine other children of Ebenezer and Parnell, neither do they report that Parnell died within two years after the last child (and before the publications of the family histories).
Ms Taylor, as a direct descendant of Rev Dan; and who purports to possess personal memorabilia of the Reverend, has given a more credible explanation than any other available. Certainly, she is subject to challenge but not with unsupported and grossly erroneous reports.