I have amended Mary Need's profile, with such sourcing as Richardson gives, and with links to English Quaker records, and also slightly edited the bio of Edmund Cartledge. Richardson actually says very very little, and all he says is on Mary's profile.
Given the marriage date of Edmund and Mary in Nottingham, England (28 Jan 1683), it would seem fairly clear that they cannot have been in America on 8 February 1683, so it would appear that either any American record of that date is wrong, or the year has been misread, or the record is referring to a different Edmund.
If anyone can track down copies or abstracts of the 1701 will of Mary's father or the 1703 will of her husband, that may cast light on the family. Richardson names Mary Need's children as John, Edmund and Mary but gives no information about them beyond that the family went at an unstated date to Pennsylvania.
I will leave those more expert than I am in American sources to take things further forward.