What we need to answer this question properly is an American source of the tune that the creator of "Wondrous Love" would probably have had access to. We have no answer to that in what's been presented here so far.

Has anybody indexed 18th and early 19th century songbooks circulating in America? Burns's version of "Ye Jacobites By Name" would certainly have been available, but the pattern of its words is not as close to "Wondrous Love" as one of the "Jack Hall" family.