Since posting that query I have discussed the situation with Ralph Odell Ward, who as I understand it, is the most knowledgable person around in regard to this Ward family. His information was to the effect that my 3-great grandmother was definitely not the same person as the Elizabeth English who married Frank. B. Ward. He also said that he could not place her in the tree of this family, though there was very much not known about that tree in the preceding generations and that she could very well fit somewhere.
My own personal evaluation... or "guess" would be that there is at least a 50/50 chance that she is a member of that family of Wards; but at this point no one that I know of has any specific information about her one way or the other, whatsoever.
If anyone comes across such information in the future I would be very interested in hearing about it, but at this point I am at a complete loss as to any idea as to how I could stir any up. I just flat "haven't got a clue". When I go to the next annual Davis family reunion, I will ask any James Monroe Davis ancestors that show up about their knowledge of wider Ward family connections... but I have little expectation that I will discover anything pertinent that way.