Thank you for the very interesting profile that you posted re James Atherton. However, whilst I cannot cement a relationship between Humphrey & James in Lancashire,I may be able to help you with James.
To begin, whilst there is no reason why you should know this, Winwick and Wigan are two 'separate' Parishes. There are records for persons named Humphrey Atherton in both of these Parishes.
Wigan In 4/10/1607 Humphrey Atherton the son of Edmund Atherton was baptised in Upholland, Wigan. However by reference to baptism registers and the Will of Edmund Atherton, Humphrey had no sibling named James. Edmund Atherton died in 1613.
There are records for other children named Humphrey Atherton in Wigan but none of these are sons of a man named Edmund.
Winwick Between 1580 and 1640 no children were baptised in the name of Humphrey Atherton in Winwick. That said, there was a family of closely related people named Atherton in Winwick. However, they demonstrated a preference for Roman Catholic worship and it goes without saying that Puritans and Roman Catholics opposed one another in religeon.
None the less, it appears to me that two perhaps three men named Humphrey had lived in Winwick in the period 1570 to 1631. One of these had moved to Bold in the Parish of Prescot by 1616.
I could find no Edmund Atherton in Winwick during the late 16th century / early 17th century.
Returning to James Atherton,your particular interest - I have copies of the church register for both Wigan and Winwick. If you wish I would be happy to examine these for a child baptised in the name of James Atherton.
Finally,I too have seen persons named Atherton recorded as 'Aderton' in England.