My information comes from Goldie Satterlee Moffatt's genealogy work on the Satterlee/ley/ly lineage.The following is from her Supplement to Vols. I and II, 1972.
Amos was the son of John (II) and Hannah [Hyde] Satterlee.John (II) was the son of John (I) and Experience [Lamphere] Satterlee.John (II) was born in 1745 at Westerly, RI, and he and Hannah were married at Hopkinton (which is right next door), but they (along with other members of the Westerly SDB group) migrated to New York State.John (II) died in NY in 1829 and Hannah died there in 1841.
Amos was born about 1785 at Salisbury, Herkimer Co., NY.Goldie shows an estimated birth date of 1781 for his wife, Lucy Dye, but no information about her parents.In fact, Goldie wasn't absolutely sure that Dye was her surname, but it sounds as though you are pretty sure about that.
It would make sense that the Dyes migrated to NY along with the Satterlees, Lampheres, and others of the SDB church.
There are some other Dyes who intermarried with the Satterlees on whom Goldie has some information.I'll come back and post more later.