After more than a century and a half of association with the tribe, wouldn't there have been some intermarriage between the blacks and the Cherokee to put the current "black Cherokees" over the 1/8 threshold or was strict marriage segregation the custom?
I don't have a dog in this fight. Just asking.
To become a member of the tribe one need only prove an ancestor was on one of the early rolls, i.e. The Dawes Rolls, used to give members their allotments. Blood quantum is not a factor. I am 1/64 and just recently joined. This is not unusual for people, like myself, who research their family history. A large number of the tribe do not get, nor want, the freebies. Any black whose ancestor intermarried & was on the rolls will remain in the tribe or can enroll if not already a member.
Hope that helps you........