In reply to your question, my grandmother Mildred Everest was a 1st cousin of David Clark Everest, who commissioned the book tracing the Everest family.
His father, John Henry Everest, and my grandmother's father, Frank Oscar Everest, were brothers. Their father was David Oscar Everest (born in Palatine,NY in 1825, anddied in 1904 in Pine Grove, Michigan) and their mother was Reliance Strong, also originally from NY.
My grandmother helped with the compiling of the book by providing information from our family Bible.
Theodore L. Everest was born in Plattsburg, NY in 1815 and died in Carson City Michigan in 1907.He appears to be from an different branch of the family.If you get the book, it will probably help you establish the link. As far as I can tell, it goes back to the mid 1700's.