Unfortunately I think most of us are involved with our own work. Over the last 18 years or so, I've corresponded with countless Carroll's who had the same family rumor that Charles Carroll of Carrollton was an ancestor. We had the same story being spouted off by some of my relatives as well, which is what caught my interest a long time ago. I started researching our family line and the family of CCof C with the expectation of meeting up somewhere in the middle. Well, that didn't happen. Then I thought that possibly we were connected in some round about way to the good Charles and I expanded my research on his family structure. I presently have 962 individuals associated with this family line. Not a whole lot, but enough that I can usually tell if a Carroll line is connected to the Charles Carroll line. That is if the Carroll family in question already has their documented line back to the mid or early 1800s. (not a difficult thing to do nowadays) I've been contacted by four people, to date, that are connected to the Charles Carroll family structure in some way. One of whom, descended from a granddaughter of Charles Carroll of Carrollton. There are a good many that could connect their ancestry to this man but not directly and not when their last name is Carroll. It is possible that there are Carrolls around today that descend from Charles Carroll the settler, the grandfather of CC of C or an even older branch.
So it's entirely possible that you are connected to this line of Carrolls. But when I checked the web site; http://carrollfamily.accessgenealogy.com/literluna.html
, containing a family genealogy that you posted as your documentation that you are in fact descended from this line, I found numerous errors related to the Carroll genealogy posted. If I were you, I would be suspicious of anything posted on this site related to the Carrolls and how you connect to them without checking it further. One thing I'd like to point out about the information listed there is that the father of Charles Carroll of Carrollton is Charles Carroll of Annapolis and his father was Charles Carroll "the immigrant", "the settler" & "the attorney general" Not the (THOMAS?) CARROLL they have him attached to.
I am curious what documentation or source was used to affix Keane Carroll as a sibling of Charles Carroll "the immigrant, settler & attorney general" and how they arrived at his birth year of 1663. (Not that I know this to be false) Not much has ever been found out about Keane Carroll other than he stayed in Ireland, he was the father of Daniel Carroll of Upper Marlboro I 1696-1751 who was the first of his line to come to this country. It is accepted that Keane Carroll is related to the Charles Carroll mentioned but exactly how hasn't been found. A brother, an uncle or cousin, he fits there somewhere. There was nothing in Wills, other records or old family letters that placed him, that anyone has found. So I'd like to email the two persons listed as posting that web page to see what they might have found or how they make that connection.
You mentioned Benjamin Franklin Carroll, I've got an uncle with the same name. No connection though I'm sure.