I have an interest in the descendants of Allie and Fred Burkitt. Allie Burkitt is my grandfather's sister, so it is her ancestry that I have information about...When I started out all I knew was Allie's married name. Allie and Fred were married on 8/26/1911 in St. Clair County. (Fred would have been born about 1885.) Before I found their marriage records on IRAD, I came across a Lem Burkitt that came from that area in Illinois in the Social Security Death Index. My guess is you are right, because I know there were other Burkitts (an unusual spelling from what I have found) in Franklin, Jefferson, and surrounding counties.
Check in Jefferson County especially for your ancestors. Jefferson County has quite a bit of there census records on line.
I will e-mail you if I come across any other Burkitt information. Let me know if you find anything.
Kathy