We have the Puritan Great Migration project for the immigrants. Those people had children after arrival, but, if I read the PGM project guidelines correctly, we shouldn't include the children in the PGM project. Just as with the Immigrants, there are MANY profiles for the early generations after the immigrants and lots of merging is still needed, Many of these have been (inappropriately) placed in the PGM project, and I have done it myself, but they are not part of that project and don't belong there. In fact, most don't qualify for any current project.
What about creating a project for the people born in New England with a cut off date of, say, born before 1700? We don't have an "Early New England Families Project," but it seems that would be an appropriate designation for them. Of course, if these people more appropriately fit in another category, such as Mayflower, William Penn, New Netherland, etc., they would be placed there.
One of the advantages to having such a project would be that profiles for early New England people could have project protection. These generally are historically-significant people and/or very common ancestors, but they currently don't qualify for project protection under any current project.