Donna, I am afraid that at this date in time, only Y-DNA analysis holds the scientific evidence as to which of the several Abernethy lines Charles Burke Abernethy may have actually belonged. Alas, while our DNA project does have data on 13 individuals (with 3 more now pending), including an individual whose descent was traced back to Nathan Abernathy and Eve Cline, we do not yet have data on anyone whose paper trail leads back to any of the other possibilities you listed, including the James S. Abernathy about whom Edward E. Smith Jr wrote. As stated, we currently have 3 volunteer's test results pending, each of whom may or may not match any of the 4 distinct lines we've so far accumulated data on, and we still have two volunteers with only 12 marker results, both with paper trails back to Ireland.
Limited Y-DNA tests such as the inexpensive 12 Marker test at Family Tree DNA do not, CANNOT, prove a relationship, despite the fact that some surname projects are using them exclusively. They only show when an individual is NOT a match with someone else. To demonstrate true matches and close relationships, it is necessary to test a minimum of 30 or more specific DYS markers from each volunteer with which to compare against another volunteers' data. Our project currently has test results from at least 3 different test labs but with the exception of the 12 Marker FT DNA results, all three labs tested for a sufficient number of identical DSY markers for a match to be determined or ruled out.
In one group all individuals have in excess of 32 markers and none have more than 2 that differ from any other individual's data in the group, demonstrating a close relationship of all in that group to a common ancestor who probably lived no later than 1500. Paper trails vary but none go back beyond about 1630. In another group, we do not yet have enough volunteers to define what is the profile for the group. We feel that it takes a minimum of 5 or more to do so, and we only have 3 in that group at present, one of whom has only a 12 Marker test results. Upgrade had been advised, but not yet achieved. The data we have on the individual with a paper trail back to Nathan and Eve Cline Abernathy had so many non-matches when compared with everybody else's data to date that he was placed in a group all by himself, as is another individual whose limited test results also show an insufficient match to be included in any of the above groups.
We certainly cannot force anyone to opt for Y-DNA testing, which typically costs around $180 and can take up to a month or more before results are known. All we can do is see to it that when Y-DNA results are known and communicated to us, they appear on the website of our Abernethy/Abernathy DNA project, appropriately catagorized in the group to which they belong, if any.