I don't think I'm being too far fetched here, but there is a good probability that your Campbells are from N. Ireland and related to Lord Neil Campbell who settled part of E. Jersey ca. 1680. He was the brother of the martyred Duke of Argyll who supported James Scot, Duke of Monmouth, in contention for the British throne against James II. Monmouth was defeated at the battle of Sedgemoor and many of his supporters fled to N. Ireland and the US, including Campbell. As a result of the E. Jersey colony (Perth Amboy area), Edinburgh Scots, Scottish Quakers, and Ulster Scots immigrated to E. Jersey. They were joined apparently by Quakers from Rhode Island which, it appears, included my Worden family, and I think Reeds were also part of that group. Or the Reeds may have been Scottish or Ulster Quakers. The original Hendersons were from Ulster and also settled E. Jersey. In the 1840s or '50s, NY businessmen invested heavily in Black Hawk's former lands which is likely why so much of northern NJ immigrated to Henderson Co.
You might want to look at the book Scotland's First Colony by Ned Landsman. The deed for E. Jersey is online via the Avalon project at Yale. See witness John Worden, secty. to James II. Campbell bought land from Lord Carteret's widow, as I remember.
Most likely your Campbells were part of either the group from County Antrim or Donegal, along with the Beresfords, Gibbs, Stevensons, Moores, Hannas, Boyds, and more.
The NJ Campbells are also the soup folks. See also Mary Mc's entries. She's a Stevenson-Gibb.