they are a very interesting family with substantial roots. as for moving to Rumney, in "The History of Plymouth NH" pp 311-313, William the Younger's bio has this: In March, 1795, William Greenough with his fine horses, his loving wife, and ten obedient children removed to Rumney, where he d. June 6, 1836. His wife d., accidentally burned, Jan. 24, 1829. So maybe young William followed his father to Rumney or vice versa?? Do you happen to know the parents of the elder William who married Judith Chase? I have not been able to sort out all the Greenoughs.
According to “New England Marriages Prior to 1700”, there are five marriage records in which a William Greenough is listed. And one of them was married three times.
As if that weren’t enough, there are four more Greenoughs listed and a Robert Greenow, which is an alternate spelling for Greenough. Any one of these could be the father of William Greenough the elder. Do you have any info for us?