I have found references in the US to Humphrey Atherton, born 1607 in Preston Lancaster, Minwick, England, married Mary Rudd then Mary Wales, 1627, died in Dorchester, Massachusetts, 16Sept. 1661. He had a daughter named Margaret. The dates would work if the Humphrey you mention were 'our' Humphrey's father, and it would be fitting if he had named his daughter after his Mother. But this is speculation. Thought perhaps the Americans might have got Prescot and Preston confused? Don't know what to make of the 'Minwick".
Thanks for all ofyour extremely thorough research!