If you go over 9 passengers (might be over 8 with SW) on a single record you are now a group and need to deal with the group dept. They are not always as reachable as the normal res agents and any changes might be harder to make.
Just co-ordinate with the other families, or designate one person to check everyone in by opening separate windows for each reservation on one computer. Still might not get boarding numbers close to each other, but even EBCI would most likely separate you too.