It's good you put a date on this question. It wouldn't have been fair if you hadn't. But there are still slight problems. The Big East wasn't around until 1979. And the Big 8 merged with the SWC around 1995, so do you use the Big 8 stats with the Big 12??
I guess to answer your question, I would put them in this order since 1960:
If the Big East wasn't around since 1979 then you would have to do the Big East since '79 until now.
Use all of the schools that are from the Big 8 and the SWC together to decide on the history of the Big 12.
I'd agree with your list. The only reason why the ACC is afloat is because of Duke and North Carolina. But they are probably the best when it comes to tradition.