Tawil means tall. Do you mean that only Tawils who are Cohanim go back to Eli? There must be some Tawils who are not Cohanim considering that Jews were probably taller and healthier than Arabs and many were called Tawil which then became a surname. Maslatons as in Ahi Ezer are Cohanim? This I did not know.
I do not doubt that names in every community got taken by other families. In my community, this was done to fool the not-too-bright KGB as well as to obtain Polish passports which facilitated escape from the old USSR.