I have just connected Henry Rand Sr. as the son of Robert Rand III ( https://www.wikitree.com/wiki/Rand-816
). It makes perfect sense with the evidence now at hand.
I have also been disentangling their ancestry from that of Robert Rand of Charlestown, Massachusetts, who was actually from Essexshire (not Suffolk). It seems that there were two different men named Robert Rand (both having wives named Alice) coming to Massachusetts around the same time. They have therefore been confused for a very long time, even by eminent genealogists. It is somewhat similar to the case of the two men named George Clark of Milford, Connecticut (both with wives named Sarah, and contemporaries). But this case with the Rand family is a bit less messy since they were living in different towns). Nevertheless very confusing, until the recent discovery that Robert Rand of Charlestown actually came from Essexshire.
Anyway, if Henry Rand can be shown to have connections with the Rand family of Charlestown (instead of Lynn), that would certainly create a need for reconsideration. However, given the evidence linking him to Zechariah Rand of Lynn, I very much doubt that any connections of Henry Rand exist with the Rands of Charlestown.