I agree that we may have come to a point where further research into the spelling of these individual's last name may offer no definitive answer. I see where you are coming from RJ. Perhaps where there is a lack of evidence we should go the route of consistency or commonality as opposed to finding an agreed upon "correct" spelling. McCartney uses Bailey to group them all together alphabetically. Perhaps we should take the same approach here. There are more than 12k profiles in Wikitree that use the Bailey spelling. Most of these profiles appear to be from the late 19th - 20th century period. There are little more than 400 Bayley profiles. This seems to be an older spelling with most of these profiles in the 17th to 19th period.
Why are there so many discussions in G2G over one little data field in a Wikitree profile ? Is this just a case of "much ado about nothing " ? Evidently we put a great deal of importance on getting the LNAB right. Wikitree has this to say about LNAB:
"The Last Name at Birth (LNAB) is significant on WikiTree."
"An LNAB should never be changed unless you have a high degree of confidence that the name you're changing it to is correct."
"If you are uncertain whether the current LNAB is correct (e.g. you think that "Smith" is probably wrong but you don't know what it should be), explain your uncertainty in the text of the profile and leave the LNAB as-is."
Obviously, in the case of a merge we can't leave the LNAB as is even if we do not know what it should be. My thought is that it would provoke fewer discussions on the "correct" LNAB if there were some written guidelines for handling those questions. Perhaps as RJ seemed to say, in a case where no amount of additional digging is going to produce a "correct" answer we use a grouping or relational approach.
Sorry for not staying on point. In Mary Bayley's case I'm thinking we should use the Bayley spelling because the majority of the documents I came across which cited a primary source used the Bayley spelling. For this profile the approach I am proposing is to use a spelling that is most consistent with the best sources available and group her and her father with the other 400 or so Bayley profiles.