1) The original surname would have been Piat.Piatt, Pyatt, etc. are all Anglicized versions of the French name.The English commonly doubled final consonants and chaned "i" to "y" when bringing French names and words into the English language.
2) Do you really think this will proved a common ancestor?I doubt it.Many of the Piats and variants today could be from unknown or unrecorded adoptions; a child fathered by someone other than the husband--it happend even in the good old days; or slaves who took the masters surname; and who knows how many other possibilities. And as your anouncement notes their are other varinant spellings that obviously have different origin.Are you prepared to help and counsel people who might find out they are not who they thought they were?Just something to consider.
It is unlikely then that this method will resolve the long standing conflict over who the original ancestor was especially the wholeJohn of France issue.I believe most of the modern research has disproved that theory, but it lingers because far too many of us are lazy in our research and we simply copy what others have done without checking the sources.