The Alexander Means attribution seems to come from Lomax's notes to WHITE SPIRITUALS from The SACRED HARP (pdf):

Wondrous Love (Track 5 & 6) Joyce Smith speaks; and then sings "Wondrous Love." This hymn is a member of the "Captain Kidd" family, so called because the ballad of "Captain Kidd" is set to one form of the tune. The "Captain Kidd" type has for several centuries been responsible for a very large number of beautiful songs, including "The Wars of Germany," "Johnny, I Hardly Knew Ye," "Sam Hall," and "Sugar Babe." This text is attributed to Rev. Alexander Means, a Methodist minister of Oxford, Georgia, and has been published again and again by Sacred Harp songbook compilers. Mrs. King Roberts conducts.