I've been sort of looking at this Jeremiah Brown - Elizabeth Moody family for a bit because I'm trying to figure out if there's a particular reason they named their third son Amos. Elizabeth Moody Brown appears to have had a nephew John Moody (thought to be the son of Clement Moody Jr.) who named his first born Amos. Its a name not really associated with the early Clement Moody families, so I've been trying to see if it was a common name in the Brown family - but it doesn't seem to be.
I haven't been able to find out much about the family other than the names of the children. Since you Jacob was born in 1757, I think you may be missing a generation in-between since Elizabeth Moody Brown was born in 1706. Having a child at 51 years is possible, but I'd rather guess you might want to look at one of her sons. Clement Brown b. 1729, Amos Brown b. abt. 1730, Joshua Brown b. abt. 1734, Simon Brown b. abt. 1735, Jeremiah Brown Jr. b. abt. 1738, Moody Brown, b. abt 1739. ( I have three daughters listed for Jeremiah and Elizabeth - Abigail b. 1727, Mary, b. 1732, and Sarah. b. 1741)
I have in my records the last two children being born in Saco. That would mean the family must have moved to Maine about 1738/39.
It also appears that Jeremiah and Elizabeth's final residence was North Yarmouth, Maine. I have yet to determine the significance of North Yarmouth during the mid 1700s, but there seems to be a fairly large number of families that passed through there at that time - and some stayed. Many of the first settlers of Friendship (Meduncook), Maine arrived there via North Yarmouth. Off the top of my head are the surnames Wadworth and Mckieff.