Hi Roger:
Wish I could help you but that would be way out of my league. All I can do is cheer from the sidelines.
In terms of what I might be able to help with, I've been toying with getting back on ancestry, after about two years of cold turkey, in order to go at this from another tangent. If I can find a sibling of James F., they could possibly provide another route to JF's parents.
In the WCD, living with James F. Burke in Cincinnati is often shown an Alice Burke, wife of Charles Burke. Charles sometimes is with his wife and JF, sometimes he's living elsewhere. Have no idea if Charles is a brother to JF, or son, how old they are, etc. Anyway, all searching on FamilySearch for the couple bear no certain results, so Ancestry is the logical next step. Will have to wait 'til my cash flow improves a bit, hopefully in a month or so, and will let you know when I do so.
Regards,
Joe