Richard, I don't know who "Edward Ballinger Price" might be. Here is the reference from Roud above:
Source Helen Hartness Flanders Collection (Middlebury College, Vermont) D46 A 13
Performer Price, Edward Ballinger
Place collected USA : Rhode Island : Newport
Collector Flanders, Helen Hartness
This looks like it is at Middlebury College. All I've had access to is Flanders' ANCIENT BALLADS TRADITIONALLY SUNG IN NEW ENGLAND, Vol. III (1963). It does say that these are"From the Helen Hartness Flanders Ballad Collection Middlebury College, Middlebury, Vermont."
The version from Ms. Price was collected by "M. Olney" and according to the entry above the one from Mr. Price was collected by H.H. Flanders herself. As near as I can tell there is no mention of Mr. Edward Ballinger Price in Vol. III of ANCIENT BALLADS. I'm afraid the answer to this lies buried somewhere at Middlebury College, unless someone out there has discovered otherwise.
I am aware that Flanders had published at least five other collections of folk songs/ ballads from the New England region. I had assumed that there was a lot of overlapping and repeating among these publications and that the ANCIENT BALLADS was the final and definitive version of things. That may not be an accurate assumption at all. I don't know very much about this. When I get back to the library, I will try to check out some of these other books to see what's going on there.