This is a citation from the DV-2011 Instructions:
"You must have either a high school education or its equivalent...
A "high school education or equivalent" is defined as successful completion of a twelve-year course of elementary and secondary education in the United States or successful completion in another country of a formal course of elementary and secondary education comparable to a high school education in the United States. Only formal courses of study meet this requirement; correspondence programs or equivalency certificates (such as the G.E.D.) are not acceptable"
From this above, I think that they are specifically stating the 12-year course of elementary and secondary education as the only equivalent to a high school education. If that's the case than it doesn't matter if your aggregated education surpasses the 12-year course. The only ones that can give you a definite answer to your dilemma are those from the KCC so consider e-mailing them or perhaps giving them a call would be better.
What about the work experience option, have you checked if you qualify through that?
My friend completed High School in the US (in school, not online) at the age of 14 so she never did the 12 years of HS and she is in College as a Junior. She showed her HS diploma and had sent her HS transcript in the package and was not asked any questions about it, but she was asked about her College credits since she had filled out a certain amount of credit hours based on what she would have at the end of last semester but when she sent her College transcript it showed less since that one was sent before the semester was over....
IMO it has to be the equivelent of HS and it doesn't matter how long it took you to get the diploma but you need to have proof of the diploma in case you will be asked.