You quote John Benjamin North as being descended from Lord Frederick North. Having been much involved in Historical and Family History research on the aristocratic Norths I do not know of such a descendant.
Lord Frederick North, 2nd Earl of Guilford had but three surviving sons by his one marriage to Anne Speke who were to become the 3rd/4th/5th Earls of Guilford namely: -
Lord George Augustus North born 1757 Francis Lord North born 1761 Frederick Lord North born 1766
Only one of these sons, George Augustus 3rd Earl, had children and no sons of his survived to live as as adults
By the 3rd Earl's first marriage to Maria Frances Mary Hobart, daughter of the 3rd Earl of Buckinghamshire: -
1. Maria Married the 2nd Marquess of Bute (Two sons of this marriage died very young) No other issue.
By the 3rd Earl's second marriage to Susan Coutts daughter of Thomas Coutts (Banker): -
2. Susan, latterly Baroness North in her own right. Married Colonel John Sydney Doyle in 1835. Colonel Doyle later assumed the surname North by deed poll.
3. Georgiana died 1835 unmarried.
The Earldom of Guilford carried no right of succession to females and thus on George Augustus' death in 1802 the title devolved to his brother: -
Francis 4th Earl of Guilford who married late in life 1810 Miss Maria Boycott There were no children of that marriage so the title then devolved to: -
Frederick 5th Earl of Guilford who died unmarried and without issue.
Frederick was succeeded by his cousin Francis North as the 6th Earl of Guilford. FRancis was the son of Lord Brownlow North, half brother to Lord Frederick North the 2nd Earl and Prime Minister.
Brownlow North, latterly Bishop of Winchester, was a son of the marriage of Francis North the 1st Earl of Guilford to Elizabeth Dowager-Viscountess Lewisham.
Unlike the Earldom the Baron North title, being a Barony by writ with peculiar rules of inheritance, could be inherited by a daughter, but if more than one daughter then the title went into abeyance until only one daughter remained alive.
Thus on the 3rd Earl's death in 1802 his three daughters became co-heiresses to the title of Baron or rather 'Baroness North in her own right'.
Susan North thus only became Baroness North on the death of her surviving sister Maria, Marchioness of Bute in 1841. (The Baron North title is currently once again in abeyance as between two co-heiresses, their brother having been killed in the Second World War and died without issue)
The families of both the 6th Earl of Guilford and Susan, Baroness North are fully accounted for and I have no knowledge of John Benjamin North in their lineage in the 19th century.
I have it on good authority from someone closely related to the North family that only two transatlantic marriages have taken place in the last two hundred years between a member of the North family and a citizen of the USA and as far as he is aware, and he might be wrong, none on the line stemming from Lord Frederick North the 2nd Earl of Guilford ever emigrated to the USA in the 18th or 19th century.
If you have evidence to the contrary I would be most interested to have further details.