I recall seeing my grandmother's name in a genealogy book in the Edward Waldo house in Scotland CT some 20 years ago. I think you probably have this book.
My parents would of course love to know your sources. (Waldoing is a competitive sport or so I have found out)
They claim that they have found evidence of a Thomas Waldo , brother of Cornelius, who migrated to Virginia, then to Massachusets, then back to England,then to Ireland. This however, would not have been my line.
My parents lived in England for a numer of years on a number of occassions and the did some research there. Although you probably have found what they have, one never knows. But their info (or speculation and or documentation) seemed to go beyond the Thomas or John son of Lawrence theories.