I came back from vacation to find a nice new match at Ancestry.com. R.M. and I are double eighth cousins, as I am descended from two children of Isham and Jane Rogers Randolph — Thomas I. Randolph (1722-1788), who married Jane Cary (1751-1774), and Susannah Randolph, who married Carter Henry Harrison (1736-1793). (Thomas Randolph, Susannah Randolph Harrison, and Bettie Randolph Railey’s sister Jane Randolph married Peter Jefferson and gave birth to Thomas Jefferson.)
Ancestry estimates our relationship as 5th-8th cousins and rates the match as “Good,” meaning that we share 6-12 cM. (Which is quite high for 8th cousins, but is attributable to (1) our double lineage and (2) luck.) That’s lower than I’d ordinarily pursue, but I’ll take it.